Associate professor at the University of Lille
Member of the Laboratoire Paul Painlevé
Contact details:
Office : Département de Mathématiques, 59655 Villeneuve d'Ascq cedex, France. Batiment M3, bureau 228.
Email : stephane.malek [no spam] @univ-lille.fr
1. S. Malek, On reducible monodromies realized by reducible Fuchsian systems, Journal Dynam. Syst 5 (1999), No. 4, 509-522.
2. S. Malek, Systèmes fuchsiens à monodromie réductible, C. R. Acad. Sci. Paris, t. 332, Série I, p. 691-694, 2001.
3. S. Malek, Fuchsian systems, with reducible monodromy, are meromorphically equivalent to reducible fuchsian systems, Proceedings of the Steklov Institute of Mathematics vol. 236 (2002), p. 468-477.
4. S. Malek, On fuchsian systems with decomposable monodromy, Proceedings of the Steklov Institute of Mathematics vol. 238 (2002), p. 196-203.
5. S. Malek, On the reducibility of the Schlesinger equations, J. Dynam. Control. Syst. 8 (2002), No. 4, 505-527.
6. S. Malek, On the reducibility of Birkhoff standard forms, J. Dynam. Control. Syst. 8 (2002), No. 3, 399-412.
7. S. Malek, On the multisummability of formal solutions of linear partial differential equations, Ulmer Seminar (2003).
8. W. Balser, S. Malek, Formal solutions of the complex heat equation in higher spatial dimensions, RIMS, 1367, (2004), 95-102.
9. S. Malek, Hypergeometric functions and parabolic partial differential equations, J. Dynam. Control. Syst. 11 No. 2, (2005).
10. S. Malek, On the summability of formal solutions of linear partial differential equations, J. Dynam. Control. Syst. 11 (2005), No. 3.
11. S. Malek, On analytic continuation of solutions of linear partial differential equations, J. Dynam. Control. Syst. 12 (2006), No. 2.
12. A. Bolibrukh, C. Mitschi, S. Malek, On the generalized Riemann-Hilbert problem with irregular singularities, Expo. Math. 2006.
13. S. Malek, On the Riemann-Hilbert problem and stable vector bundles on the Riemann sphere, Groupes de Galois arithmétiques et différentiels (Luminy 2004; eds D. Bertrand et P. Debes), Séminaires et Congrès de la SMF, volume 13, 2006.
14. W. Balser, A. Duval, S. Malek, Summability of formal solutions for abstract Cauchy problems and related convolution equations, Ulmer Seminar (2006).
15. S. Malek, On the summability of formal solutions of nonlinear partial differential equations with schrinkings, J. Dynam. Control. Syst 13 (2007), No. 1.
16. S. Malek, On functional linear partial differential equations in Gevrey spaces of holomorphic functions, Annales de Toulouse, 6, 16 no. 2, 2007.
17. S. Malek, On singularly perturbed partial integro-differential equations with irregular singularity, J. Dynam. Control. Syst 13 (2007), No. 3.
18. S. Malek, On the Stokes phenomenon for holomorphic solutions of integro-differential equations with irregular singularity, J. Dynam. Control. Syst 14 (2008), no. 3.
19. S. Malek, Complex singularity analysis for linear q-difference-differential equations, J. Dynam. Control. Syst 15 (2009), no. 1.
20. S. Malek, Gevrey functions solutions of partial differential equations with fuchsian and irregular singularities, J. Dynam. Control. Syst 15 (2009), no. 2.
21. S. Malek, On Gevrey asymptotics for some nonlinear integro-differential equations, J. Dynam. Control. Syst 16 (2010), no. 3.
22. S. Malek, Singularly perturbed q-difference differential equations with irregular singularity, J. Dynam. Control. Syst 17 (2011), no 2.
23. S. Malek, C. Stenger, On complex singularity analysis of holomorphic solutions of linear partial differential equations, Adv. Dyn. Syst. Appl. vol. 6, no. 2 (2011).
24. S. Malek, Summability of formal solutions for doubly singular nonlinear partial differential equations, J. Dynam. Control. Syst. 18 (2012), no. 1.
25. A. Lastra, S. Malek, On q-Gevrey asymptotics for singularly perturbed q-difference-differential problems with an irregular singularity, Abstract and Applied Analysis vol. 2012, Article ID 860716, 35 pages, 2012.
26. A. Lastra, S. Malek, J. Sanz Gil, On q-asymptotics for q-difference-differential equations with Fuchsian and irregular singularities, Journal of Differential equations vol. 252, Issue 10 (2012).
27. A. Lastra, S. Malek, J. Sanz Gil, Continuous right inverses for the asymptotic Borel map in ultraholomorphic classes via a Laplace-type transform, Journal of Mathematical Analysis and Applications, vol 396, no. 2 (2012).
28. S. Malek, Parametric Stokes phenomenon for solutions of singularly perturbed linear partial differential equations, Abstract and Applied Analysis, vol. 2012, Article ID 930385.
29. A. Lastra, S. Malek, J. Sanz Gil, On q-asymptotics for q-difference-differential equations with Fuchsian and irregular singularities. Formal and analytic solutions of differential and difference equations, 73--90, Banach Center Publ., 97, Polish Acad. Sci. Inst. Math., Warsaw, 2012.
30. S. Malek, On complex singularity analysis for linear partial q-difference-differential equations using nonlinear differential equations, J. Dynam. Control. Syst. 19 (2013) no. 1.
31. A. Lastra, S. Malek, J. Sanz Gil, On Gevrey solutions of threefold singular nonlinear partial differential equations, Journal of Differential Equations, vol. 255, Issue 10 (2013).
32. A. Lastra, S. Malek, C. Stenger, Complex singularity analysis for some linear partial differential equations in C^3, Abstract and Applied Analysis, vol. 2013, Article ID 394564.
33. S. Malek, On singularly perturbed small step size difference-differential nonlinear PDEs, Journal of Difference Equations and Applications, vol. 20, Issue 1 (2014).
34. A. Lastra, S. Malek, On parametric Gevrey asymptotics for singularly perturbed partial differential equations with delays, Abstract and Applied Analysis, vol. 2013, Article ID 723040.
35. A. Lastra, S. Malek, On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces, Abstract and Applied Analysis, vol. 2014, Article ID 153169.
36. A. Lastra, S. Malek, J. Sanz Gil, Summability in general Carleman ultraholomorphic classes, Journal of Mathematical Analysis and Applications, vol. 430 (2015).
37. A. Lastra, S. Malek, Parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems, J. Differential Equations 259 (2015), no. 10.
38. A. Lastra, S. Malek, On parametric multisummable formal solutions to some nonlinear initial value Cauchy problems, Advances in Difference Equations 2015, 2015:200.
39. A. Lastra, S. Malek, On parametric multilevel q-Gevrey asymptotics for some linear q-difference-differential equations, Advances in Difference Equations (2015) 2015:344.
40. A. Lastra, S. Malek, Multi-level Gevrey solutions of singularly perturbed linear partial differential equations, Advances in Differential Equations, vol. 21, Number 7/8 (2016).
41. A. Lastra, S. Malek, J. Sanz Gil, Strongly regular multi-level solutions of singularly perturbed linear partial differential equations, Results in Mathematics, vol. 70, Issue 3-4, Nov. (2016).
42. A. Lastra, S. Malek, On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference differential initial value Cauchy problems, Journal of Difference Equations and Applications, vol. 23, issue 8, 2017.
43. S. Malek, On singular solutions to PDEs with turning point involving a quadratic nonlinearity, Abstract and Applied Analysis, vol. 2017, Article ID 9405298, 2017.
44. S. Malek, Parametric Gevrey asymptotics for a q-analog of some linear initial value problem, Funkcialaj Ekvacioj 60 no. 1 (2017).
45. A. Lastra, S. Malek, Some notes on the multi-level Gevrey solutions of singularly perturbed linear partial differential equations. Analytic, algebraic and geometric aspects of differential equations, 415--427, Trends in Math. Birkhauser/Springer, Cham, 2017.
46. A. Lastra, S. Malek, Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity, Electron. J. Differential Equations, Vol. 2018 (2018), No. 46.
47. A. Lastra, S. Malek, Parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms, Advances in Difference Equations (2018), 2018:386.
48. A. Lastra, S. Malek, On parametric Gevrey asymptotics for some initial value problems in two asymmetric complex time variables, Results in Mathematics, Vol. 73, No. 4, 2018.
49. A. Lastra, S. Malek, Multiscale Gevrey asymptotics in boundary layer expansions for some initial value problem with merging turning points, Advances in Differential Equations, vol 24, No. 1-2, 2019.
50. A. Lastra, S. Malek, Parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms, Electron. J. Differential Equations, Vol. 2019 (2019), No. 55.
51. A. Lastra, S. Malek, Some notes on the parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms, Complex Differential and Difference Equations: Proceedings of the School and Conference held at Bedlewo, Poland, September 2-15, 2018 (pp. 435–446). Berlin, Boston: De Gruyter, 2019.
52. T. Dreyfus, A. Lastra, S. Malek, Multiple-scale analysis for some linear partial q-difference and differential equations with holomorphic coefficients, Advances in Difference Equations, 2019:326, 2019.
53. A. Lastra, S. Malek, On a q-analog of a singularly perturbed problem of irregular type with two complex time variables, Mathematics 2019, 7(10), 924; 2019.
54. A. Lastra, S. Malek, On parametric Gevrey asymptotics for some nonlinear initial value problems in symmetric complex time variables, Asymptotic Analysis vol. 118, no. 1-2, 2020.
55. S. Malek, On a partial q-analog of a singularly perturbed problem with Fuchsian and irregular time singularities, Abstract and Applied Analysis, vol. 2020, Article ID 7985298, 2020.
56. A. Lastra, S. Malek, Boundary layer expansions for initial value problems with two complex time variables, Advances in Difference Equations 2020, 2020:20.
57. S. Malek, On boundary layer expansions for a singularly perturbed problem with confluent fuchsian singularities, Mathematics 2020, 8(2), 189.
58. S. Malek, On inner expansions for a singularly perturbed Cauchy problem with confluent fuchsian singularities, Mathematics 2020, 8(6), 976.
59. G. Chen, A. Lastra, S. Malek, Parametric Gevrey asymptotics in two complex time variables through Truncated Laplace transforms, Advances in Difference Equations, 2020, 2020:307.
60. A. Lastra, S. Malek, Singularly perturbed linear initial value problems with mixed irregular and Fuchsian time singularities, J. Geom. Anal. 30 (2020), No. 4.
61. G. Chen, A. Lastra, S. Malek, On Gevrey asymptotics for linear singularly perturbed equations with linear fractional transforms, Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat., RACSAM 115, No. 3, Paper No. 121, 2021.
62. S. Malek, Asymptotics and confluence for some linear q-difference differential Cauchy problem, Journal of Geometric Analysis 32, (93) 2022.
63. G. Chen, A. Lastra, S. Malek, Some Notes on the Parametric Gevrey Asymptotics in two Complex Time Variables through Truncated Laplace Transforms, volume "Formal and Analytic Solutions of Differential Equations : Proceedings of the webconference FASNET organized in Alcala, Spain, June 29th to 30th 2020. World Scientific Publishing Europe Ltd. 2022.
64. S. Malek, Asymptotics and confluence for a singular nonlinear q-difference-differential Cauchy problem, Abstract and Applied Analysis, vol. 2022, Article ID 9637628, 2022.
65. S. Malek, Double-scale Gevrey asymptotics for logarithmic type solutions to singularly perturbed linear initial value problems, Results Math. 77 (2022), no. 5, Paper No. 198.
66. S. Malek, Small divisors effects in some singularly perturbed initial value problem with irregular singularity, Analysis 2022, 0, doi:10.1515/anly-2022-1077.
67. S. Malek, Gevrey asymptotics for logarithmic type solutions to singularly perturbed problems with nonlocal nonlinearities, Abstract and Applied Analysis, vol. 2023, Article ID 3025513, 2023.
68. A. Lastra, S. Malek, On q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations, Math. Ann. 390, No. 1, 2024.
69. S. Malek, Double-scale expansions for a logarithmic type solution to a q-analog of a singular initial value problem, Abstract and Applied Analysis, vol. 2024, Article ID 8904337, 2024.
70. A. Lastra, S. Malek, Gevrey versus q−Gevrey asymptotic expansions for some linear q−difference-differential Cauchy problem, Results in Mathematics , 0.1007/s00025-024-02250-z, 2024.
71. S. Malek, Parametric asymptotic expansions and confluence for Banach valued solutions to some singularly perturbed nonlinear q-difference-differential Cauchy problem, to appear in Izvestiya : Mathematics, Special volume dedicated to Andrey Bolibrukh, 2026.
72. A. Lastra, S. Malek, On parametric 0-Gevrey asymptotic expansions in two levels for some linear partial q-difference-differential equations, to appear in Analysis and Mathematical Physics, 2025.
73. S. Malek, On summable formal power series solutions to some initial value problem with infinite order irregular singularity and Mahler transforms, preprint 2024.
74. G. Chen, A. Lastra, S. Malek, Parametric formal Gevrey asymptotic expansions in two complex time variable problems, preprint 2025.
75. S. Malek, Ramified asymptotic expansions for some linear initial value problem with Mahler transforms, preprint 2025.
76. A. Lastra, S. Malek, On some q-analog of an initial value problem with infinite order irregular singularity and Mahler transforms, preprint 2025.
1) August, 21 2000 : International Conference on Differential equations and dynamical systems, Suszdal (Russia). Title of the talk : On Fuchsian systems with reducible monodromy.
2) September 10, 2000 : Workshop "Monodromy and differential equations in singularity theory and groups representations " (INTAS program 97-1644), Steklov Institut in Moscow (Russia), organized par A.A. Bolibrukh et C. Sabbah. Title of the talk : On meromorphic equivalence of Fuchsian systems with reducible monodromy.
3) September 10, 2001 : Seminar at the Steklov Institut of Moscow (Russia). Title of the talk : On Fuchsian systems with decomposable monodromy.
4) February 1st, 2002 : Seminar at the University of Angers (France). Title of the talk : Sur la réductibilité des équations de Schlesinger.
5) September 25, 2002 : Seminar at the Steklov Institut of Moscow (Russia). Title of the talk : On the generalized Riemann Hilbert problem and reducibility of differential systems with irregular singularities.
6) March,11 2003 : Seminar "Equations fonctionnelles" at the University of Strasbourg (France). Title of the talk : Sur la multisommabilité de solutions formelles d'EDP linéaires à coefficients constants.
7) March 21, 2003 : Workshop organized by B.L.J. Braaksma. University of Groningen (Netherlands). Title of the talk : On the multisummability of formal solutions of linear PDE.
8) December, 9 2003 : Seminar at the University of Groningen (Netherlands). Title of the talk : On the Riemann-Hilbert and the Birkhoff problems.
9) January, 28 2004 : Seminar at the "Ecole Normale Supérieure de Lyon" (France). Title of the talk : Equations de Schlesinger et réductibilité.
10) March, 11 2004 : International conference on "arithmetical and differential Galois groups", CIRM, Luminy (France) Title of the talk : On reducible Fuchsian systems and their deformations.
11) March, 16 2004 : Seminar "Equations fonctionnelles" at the University of Strasbourg (France). Title of the talk : Sur la sommabilité de solutions formelles d'équations aux derivées partielles linéaires.
12) January, 12 2005 : Seminar at the University of La Rochelle (France). Title of the talk : Sommabilité de solutions formelles d'équations aux dérivées partielles linéaires et non linéaires}.
13) November, 22 2005 : Seminar "Equations fonctionnelles" at the University of Strasbourg (France). Title of the talk : Equations integro-differentielles singulièrement perturbées.
14) June, 12 2006 : Workshop on difference and q-difference equations. University of Ulm (Germany). Title of the Talk : On q-Gevrey holomorphic solutions of functional linear PDEs.
15) June, 21 2007 : Seminar at the University of Angers (France). Title of the talk : Sur le phénomène de Stokes pour des solutions holomorphes d'équations intégro-différentielles à singularité irrégulière.
16) November, 27 2007 : Seminar "Equations fonctionnelles" of the University of Strasbourg (France). Title of the talk : Equations aux q-différences-différentielles dans des espaces de fonctions Gevrey.
17) January, 31 2008 : Conference at Luminy ''Holomorphic PDES, summability and small divisors'' organized by Y. Takei et L. Stolovitch. Title of the talk : Singularly perturbed PDEs with irregular singularity.
18) March, 27 2008 : Seminar at the University of La Rochelle (France). Title of the talk : Solutions ultraholomophes d'équations aux q-différences-différentielles.
19) May, 16 2008 : Seminar at the University of Limoges (France). Title of the talk : Equations aux q-différences-différentielles dans des espaces de fonctions ultraholomorphes.
20) August, 12 2008 : Conference FASDE at the Banach Center de Bedlewo (Poland) ''Formal and analytic solutions of differential equations'' organized by W. Balser et G. Lysik. Title of the talk : Complex singularity analysis for linear q-difference-differential equations.
21) October, 24 2008 : Sino-French workshop on PDEs and applications, Chern Institut, Nankai University, Tinajin (China). Title of the talk : On Gevrey functions solutions of partial differential equations with fuchsian and irregular singularities.
22) November, 11 2008 : Conference in honor of Prof. Okamoto, University of Strasbourg (France). Title of the talk : On Gevrey functions solutions of partial differential equations with fuchsian and irregular singularities.
23) June, 10 2009 : Seminar at the IMPAN, Warsaw (Poland). Title of the talk : On ultraholomorphic solutions of partial differential equations with fuchsian and irregular singularities.
24) September, 7 2009 : Seminar at the University of Rennes (France). Title of the talk : Analyse des singularités complexes d'équations aux q-différence-différentielles.
25) January, 12 2010 : Seminar at the University of Valladolid (Spain). Title of the talk : On Gevrey solutions of partial differential equations with fuchsian and irregular singularities.
26) January, 15 2010 : Seminar at the University of Valladolid (Spain). Title of the talk : On Gevrey asymptotics for some nonlinear integro-differential equations.
27) February, 18 2010 : Seminar of the University of La Rochelle (France). Title of the talk : Asymptotique Gevrey pour des équations intégro-différentielles non-linéaires.
28) March, 17 2010 : Conference in honor of Prof. Masake Miyake, University of Nagoya (Japan). Title of the talk : On Gevrey asymptotics for some nonlinear integro-differential equations.
29) June, 28 2010 : Spanish/FrenchWorkshop organized by C. Stenger at the University of La Rochelle (France). Title of the talk : Perturbations singulières d'équations aux dérivées partielles à singularité irrégulière.
30) December, 13 2010 : Spanish/French Workshop organized by J. Sanz at the University of Valladolid (Spain). Title of the talk : Complex singularity analysis for linear partial q-difference-differential equations using nonlinear differential equations.
31) June, 21 2011 : Seminar of the University of Strasbourg. Title of the talk : Analyse des singularités complexes pour des équations aux q-différence-différentielles partielles.
32) August, 11 2011 : Conference FASDE II organized by G. Lysik at the IMPAN of Bedlewo (Poland). Title of the talk : On singularly perturbed q-difference-differential equations with irregular singularity.
33) September, 13 2011 : Seminar at the University of Valladolid (Spain). Title of the talk : On singular perturbations of q-difference-differential equations.
34) April, 26 2012 : Conference Sino/french organized at the University of Wuhan (China). Title of the talk : On Gevrey solutions of threefold singular nonlinear partial differential equations.
35) June, 19 2012 : Seminar ``Analysis and operator theory '' at the Ohio State University (USA). Title of the talk : On q-Gevrey asymptotics for singularly perturbed q-difference-differential problems with irregular singularity.
36) September 12, 2012 : Workshop on differential and difference equations in the complex domain at the IMPAN, Warsaw (Poland). Title of the talk : On the parametric Stokes phenomenon for singularly perturbed linear PDE.
37) April, 25 2013 : Seminar of applied mathematics at the University of Alcala de Henares (Spain). Title of the talk : On singularly perturbed small step size difference-differential nonlinear PDEs.
38) August, 30 2013 : Conférence FASDE III organized by G. Lysik at the IMPAN of Bedlewo (Poland). Title of the talk : On singularly perturbed difference-differential nonlinear PDE.
39) October, 17 2013 : Conference ``Exponential analysis of differential equations and related topics'' organized by Y. Takei at RIMS (Kyoto, Japan). Title of the talk : On Gevrey asymptotics for difference-differential nonlinear PDEs.
40) April, 24 2014 : Seminar of applied mathematics at the University of Alcala de Henares (Spain). Title of the talk : Complex singularity analysis for linear PDEs in C^3.
41) September, 2nd 2014 : Conference FASFE organized by J. Sanz at the University of Valladolid (Spain). Title of the talk : On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces.
42) December, 1st 2015 : Seminar of Analysis at the University of Tokyo (Japan). Title of the talk : On complex singularity analysis for some linear partial differential equations.
43) December, 9 2015 : Workshop at RIMS (joint research) (Japan). Title of the talk : Parametric multisummable formal solutions to nonlinear PDEs.
44) August, 25 2016 : Conference FASFE organized by Luca Prelli and Javier Sanz at the University of Lisboa (Portugal). Title of the talk : On parametric Gevrey asymptotics for a q-analog of some linear initial value problem.
45) September, 6 2017 : Conference FASdiff17 organized by Alberto Lastra at the University of Alcala de Henares (Spain). Title of the talk : On parametric q-Gevrey asymptotics for some linear initial value problems with deviating arguments.
46) October, 31 2017 : Conference AAMDE organized by Renat Gontsov et Irina Goriushkina at the Institut Kharkevich (IITP RAS) in Moscow (RFBR-CNRS project) (Russia). Title of the talk : On twofold q-Gevrey asymptotics for a q-analog of some linear initial value problem.
47) June, 26 2018 : Conference FASPDE18 organized by J. Sanz and L. Prelli at the University of Padova (Italy). Title of the talk : On multiscale Gevrey asymptotics in boundary layer expansions for some singularly perturbed PDE.
48) September, 3 2018 : Conference ``Complex Differential and Difference Equations'' organized by G. Filipuk, G. Lysik and S. Michalik, at the IMPAN of Bedlewo (Poland). Title of the talk : On parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms.
49) September, 12 2019 : Conference FASFE19 organized by J. Sanz at the University of Valladolid (Spain). Title of the talk : On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms.
50) April, 20 2023 : Seminario Iberoamericano de Matematicas no. 120 at the University of Valladolid (Spain). Title of the talk : Double scale Gevrey asymptotics for logarithmic type solutions to singularly perturbed linear initial value problems.
51) September, 2 2023 : Conference ``Complex Differential and Difference Equations II'' organized by G. Lysik and S. Michalik, at the IMPAN of Bedlewo (Poland). Title of the talk : Gevrey asymptotics for logarithmic type solutions to singularly perturbed problems with nonlocal lonlinearities.
52) December, 9 2023 : Seminar at the University of Josai in Tokyo (Japan). Title of the talk : Two seminal results on Gevrey asymptotics for partial differential equations.
53) December, 13 2023 : Seminar at the Shibaura Institute of Technology (SIT) in Tokyo (Japan). Title of the talk : On boundary layer expansions for singularly perturbed problem with confluent Fuchsian singularities.
54) December, 15 2023 : Seminar at Chiba University in Chiba (Japan). Title of the talk : Asymptotics and confluence for nonlinear q-difference-differential Cauchy problems.
55) April, 25 2024 : Seminar at the University of Valladolid (Spain). Title of the talk : Gevrey versus q-Gevrey asymptotic expansions for some linear q-difference-differential Cauchy problem.
56) June, 18 2024 : Mini workshop organized by G. Chen at the Great Bay University, Dongguan (China). Title of the talk : Gevrey asymptotics for linear singularly perturbed equations with linear fractional transforms.
57) May, 8 2025 : Seminar at the University of Valladolid (Spain). Title of the talk : On parametric asymptotic expansions and confluence for Banach valued solutions to some singularly perturbed nonlinear q-difference-differential Cauchy problem.
58) September, 4 2025 : Conference FASdiff25 organized by A. Lastra at the University of Alcala de Henares (Spain). Title of the talk : On summable formal power series solutions to some initial value problem with infinite order irregular singularity and Mahler transforms.