Publications

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(A) research announcement

(U) unrefereed publication

(P) refereed conference proceedings

(PN) conference proceedings, not refereed

(B) book

(C) book chapter (refereed original results)

(S) survey article

For copies of articles please use Arxiv.org (https://arxiv.org/a/tintarev_c_1.html), MathSciNet or Google.

Last updated February 2020

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1. Short time asymptotics for fundamental solutions of higher order parabolic equations, Communications in Partial Differential Equations, 7 (4), (1982), 371-391.
2. (with Kimimasa Nishiwada) Lacunas and saturation properties for hyperbolic differential operators with analytic coefficients, Israel Journal of Mathematics, 49 (4), (1984), 280-306.
3. On complementary geometrical conditions of uniqueness and non-uniqueness for operators with simple characteristics, Communications in Partial Differential Equations, 11 (9), (1986), 989-1008.
4. (with Avner Friedman) Boundary asymptotics for solutions of the Poisson-Boltzmann equation, Journal of Differential Equations, 69 (1) (1987), 15-38.
5. (PN) Fundamental solution of the Poisson-Boltzmann equation, in I.W.Knowles. Y.Saito (Eds), Differential equations and mathematical physics , Springer: Lecture Notes Math.1285 (1987) 480-485.
6. On geometry of P-convex sets for operators of the real principal type, Israel Journal of Mathematics, 64 (2), (1988), 195-206.
7. (with Martin Schechter) Spherical maxima in Hilbert space and semilinear elliptic eigenvalue problems, Differential and Integral Equations, 3 (5), (1990) 889-899.
8. (with Martin Schechter) Eigenvalues for semilinear boundary value problems, Archive for Rational Mechanics and Analysis, 113 (1991), 197-208.
9. Characterization of P-convexity for supports in terms of tangent curves, Journal of Mathematical Analysis and Applications, 164 (2) (1992), 590-596.
10. (with Martin Schechter) Families of first eigenfunctions for semilinear elliptic eigenvalue problems, Duke Mathematical Journal, 62 (2), (1991), 453-465.
11. (with Martin Schechter) Points of spherical maxima and solvability of semilinear elliptic problems, Canadian Journal of Mathematics, 43 (4) (1991), 1-7.
12. Level set maxima and quasilinear elliptic problems, Pacific Journal of Mathematics, 153 (1) (1992), 185-200.
13. Mountain impasse theorem and spectrum of semilinear elliptic problems, Transactions of American Mathematical Society, 336 (1993) 621-629.
14. (with Martin Schechter) Pairs of saddle points produced by linking subsets with application to semilinear elliptic problems , Bulletin de la Societe Mathematique de Belgique, serie B, 44 (3) (1992), 249-261. Citations: 26
15. (with Martin Schechter) Nonlinear eigenvalues and mountain pass methods , Topological Methods of Nonlinear Analysis, 1 (1993), 183-201.
16. A theorem of the ’mountain impasse’ type and semilinear elliptic problems on manifolds, Journal of Differential Equations, 113 (1) (1994) 234-245.
17. (P) (with Martin Schechter) Critical points for pairs of functionals and semilinear elliptic equations, in C.Bandle, J.Bemelmans, M.Chipot, J.Saint Jean Paulin, I.Shafrir (Eds.), Calculus of variations, applications and computations, Pitman Research Notes 326 (1994), 245-253.
18. A relation between critical values and eigenvalues in nonliniar minimax problems , Applicable Analysis, 54 (1994), 57-73.
19. Critical values and miminal periods for autonomous Hamiltonian systems , Discrete and Continuous Dynamical Systems, 1 (1995), 389-400.
20. Second eigenfunctions of nonlinear eigenvalue problems, Journal of Mathematical Analysis and Applications, 196, 361-383 (1995).
21. Mountain pass and impasse for non-smooth functionals with constraints, Journal of Nonlinear Analysis -Theory, Methods and Applications, 26, 798-803 (1996).
22. Isotopic linking and critical points of functionals, Journal of Nonlinear Analysis -Theory, Methods and Applications, 30(1997).
23. (P) (with Ian Schindler) Semilinear elliptic problems on unbounded domains, in: A.Ioffe, S.Reich, I.Shaffrir (eds.), Calculus of Variations and Differential Equations, Chapman & Hall/CRC, Research Notes in Mathematics Series, Vol. 410, CRC Press, Boca Raton, FL, 2000, 210-217.
24. Solutions to elliptic systems of Hamiltonian type in RN, EJDE Vol. 1999(1999), No. 29, pp. 1-11,
25. (P) (with Ian Schindler) An abstract version of the concentration compactness principle, Nonlinear Analysis: Series A, Theory and Methods, 47 (2001), 3531-3536.
26. (with Ian Schindler) Abstract concentration compactness and semilinear elliptic equations on unbounded domains, in: M.R. Grossinho, M. Ramos, C. Rebelo, L. Sanchez, (Eds.), Progress in Nonlinear Differential Equations and Their Applications 43, Birkhäuser Boston, 2001, 369-378.
27. (with Ian Schindler) A nonlinear Schrödinger equation with external magnetic field, Rostocker Mathematisches Kolloquium 56, 49-54 (2002) Citations: 15
28. Semilinear elliptic problems on unbounded subsets of Heisenberg groups, EJDE , Vol. 2001(2001), No. 18, pp. 1-8.
29. (with Ian Schindler) An abstract version of the concentration compactness principle, Revista Matematica Complutense, 15, 1-20 (2002). Citations: 19
30. (with Ian Schindler) Semilinear subelliptic problems without compactness on Lie groups, Nonlinear Differential Equations and Applications 11 (2004), 299 - 309.
31. Singular semilinear elliptic equations in the half-space, Rend.Istit.Mat. Univ.Trieste 33 (2001), 1-11.
32. (with Karl-Heinz Fieseler) Semilinear elliptic problems and concentration compactness on non-compact Riemannian manifolds, J.Geom.Anal. 13 (2003), 67-75.
33. (with Marco Biroli and Ian Schindler) Semilinear problems on Hausdorff spaces with symmetries, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 27 (2003), 175-189.
34. (with Martin Schechter) Linking in Hilbert space, Proceedings of American Mathematical Society, 134 (2006), 403-410.
35. (with Karl-Heinz Fieseler) Sobolev minimizers on homogeneous spaces, Potential Analysis 23, 153-163 (2005).
36. (with Martin Schechter) Finding linking sets, International Journal of Mathematics and Mathematical Sciences 2006, Art. ID 24623, 13 pp.
37. Nonlinear subelliptic Schrödinger equation with external magnetic field, Electronic Journal of Differential Equations, Vol. 2004, No. 123, pp. 1-9 (2004).
38. (with Yehuda Pinchover) Existence of minimizers for Schrödinger operators under domain perturbations with application to Hardy’s inequality, Indiana University Mathematical Journal 54, 1061 - 1074 (2005). Citations: 10
39. A semilinear elliptic problem on unbounded domains with reverse penalty, Nonlinear Analysis 64 (2006), 1496-1502.
40. (with Yehuda Pinchover) A ground state alternative for singular Schrödinger operators, Journal of Functional Analysis 230 (2006), 65-77. Citations:13
41. (with Jan Chabrowski) An elliptic Neumann problem with subcritical nonlinearity, Bulletin of the Polish Academy of Sciences - Mathematics 53 (2005) 7-16.
42. (with Achilles Tertikas) On existence of minimizers for the Hardy–Sobolev-Maz’ya inequality, Annali di Matematica Pura e Applicata (4) 186 (2007), 645-662. Citations: 25
43. (with Yehuda Pinchover) Ground state alternative for p-Laplacian with potential term, Calculus of Variations and Differential Equations 28 (2007), 179-201. Citations: 14
44. (P) Concentration-compactness principle for mountain pass problems, in Proceedings of Conference on Differential and Difference Equations, August 1-5, 2005, Melbourne, Florida, Hindawi Publishing Corporation, 2006.
45. (with Ian Schindler) Semilinear elliptic equations on fractal blow-ups Journal of Mathematical Analysis and Applications, 352 (2009), 57-64.
46. (with Karl-Heinz.Fieseler) Concentration Compactness: Functional-Analytic Grounds and Applications, c. 270 pp, Imperial College Press 2007. Citations: 19
47. (with Yehuda Pinchover and Achilles Tertikas) A Liouville-type theorem for the p-Laplacian with potential term, Annales d’Institute Henri Poincaré - Analyse non-linèaire 25 (2008), 357-368.
48. (P) (with Ian Schindler) Mountain pass solutions to semilinear problems with critical nonlinearity, Discrete and Continuous Dynamical Systems 2007, Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference, suppl., 912-919.
49. (with Peter Takac) Generalized Minimizer Solutions for Equations with the p-Laplacian and a Potential Term, Proceedings of Royal Society Edinburgh Sect. A 138 (2008), 201-221
50. (P) Positive solutions of elliptic equations with a critical oscillatory nonlinearity, Discreet and Continuous Dynamical Systems 2007, Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference, suppl., 974-981.
51. (PN) Permanence of metric fractals, Proceedings of the 2006 International Conference in honor of Jacqueline Fleckinger, 185-192, Electronic Journal of Differential Equation Conferences 16 Texas State Univ.–San Marcos, Dept. Math., San Marcos, TX, 2007.
52. On scalar field equations with critical nonlinearity, J. Fixed Point Theory Appl. 4 (2008). 97-106.
53. (C) (with Yehuda Pinchover) On Hardy-Sobolev-Maz’ya inequality, in: Maz’ya, Vladimir; Isakov, Victor (Eds.), Sobolev Spaces in Mathematics, volume 1: Sobolev Type Inequalities (International Mathematical Series , Vol. 8) Springer-Verlag 2009, 281-297.
54. (C) Cocompact imbeddings and structure of weakly convergent sequences, in: Maz’ya, Vladimir; Isakov, Victor (Eds.), Sobolev Spaces in Mathematics, volume 1: Sobolev Type Inequalities (International Mathematical Series , Vol. 8) Springer-Verlag 2009, 361-375.
55. Concentration compactness at the mountain pass level in semilinear elliptic problems, NoDEA Nonlinear Differential Equations Appl. 15 (2008), 581-598
56. (with Yehuda Pinchover) On positive solutions of minimal growth for singular p-Laplacian with potential term, Advances of Nonlinear Studies 8 (2008), 213-234.
57. (with Yehuda Pinchover) On positive solutions of p-Laplacian-type equations, Analysis, Partial Differential Equations and Applications 245-267, Oper. Theory Adv. Appl., 193, Birkhäuser Verlag, Basel, 2009
58. (with Mattias Enstedt) Weighted spectral gap for magnetic Schrödinger operator with a potential term, Potential Analysis 31 (2009), 215-226.
59. (with Everaldo Medeiras and Kanishka Perera) Multiplicity results for problems involving the Hardy-Sobolev operator via Morse theory, Journal of Nonlinear Analysis – Theory, Methods and Applications 72 (2010), 2170-2177.
60. (with Adimurthi) Hardy inequalities for weighted Dirac operator, Annali di Matematica Pura e Applicata 189 (2009), 241-251.
61. (with Adimurthi) Cocompactness properties of Moser-Trudinger functional in connection to semilinear biharmonic equations in four dimensions, Matematica Contemporanea 36 (2009), 1-10.
62. (with Adimurthi) On a version of Trudinger-Moser inequality with the Möbius shift invariance, Calculus of Variations and Partial Differential Equations, 39 (2010), 203-212. Citations: 8.
63. (with Adimurthi and João Marcos do Ò) Cocompactness and minimizers for inequalities of Hardy-Sobolev type involving N-Laplacian, Nonlinear Differential Equations and Applications, 17 (2010) 467-477.
64. (with David Costa and João Marcos do Ò) Schrödinger equations with critical nonlinearity, singular potential and a ground state, Journal of Differential Equations 249 (2010), 240-252.
65. (P) Is the Trudinger-Moser nonlinearity a true critical nonlinearity? Discrete and Continuous Dynamical Systems 2011, Dynamical systems, differential equations and applications. 8th AIMS Conference. Suppl. Vol. II, 1378-1384.
66. (with Jan Chabrowski) Ground state for the Schrödinger operator with the weighted Hardy potential, International Journal of Differential Equations, International Journal of Differential Equations 2011, Art. ID 358087, 26 pp.
67. (with Michael Cwikel) On interpolation of cocompact imbeddings, Revista Matematica Complutense 26 (2013), 33-55.
68. (with David Costa and Joao Marcos do Ò) Compactness properties of critical nonlinearities and nonlinear Scrödinger equations, Proceedings of the Edinburgh Mathematical Society, 55 (2012), 1-15.
69. (with Adimurthi) On compactness in the Trudinger-Moser inequality, Annali della Scuola Normale Superiore di Pisa Cl. Sci. (5) Vol. XIII (2014), 1-18.
70. (C,S) Concentration analysis and compactness, in: Adimurthi, K. Sandeep, I. Schindler, C. Tintarev, editors, Concentration Analysis and Applications to PDE ICTS Workshop, Bangalore, January 2012, ISBN 978-3-0348-0372-4, Birkhäuser, Trends in Mathematics (2013), 117-141.
71. (U) (with Adimurthi, K. Sandeep and I. Schindler) Introduction to the volume Concentration Analysis and Applications to PDE ICTS Workshop, Bangalore, January 2012, ISBN 978-3-0348-0372-4, Birkhäuser, Trends in Mathematics (2013), pp. vii-x.
72. (with Gianni Mancini and Kunnath Sandeep) Trudinger-Moser inequality in the hyperbolic space ℍ^N, Advances in Nonlinear Analysis 2 (2013), 309-324.
73. (with Kanishka Perera) On the second minimax level for the scalar field equation, Annali di Matematica Pura e Applicata, Ann. Mat. Pura Appl. (4) 194 (2015), 131-144.
74. (with Leszek Skrzypczak) A geometric criterion for compactness of invariant subspaces, Archiv der Matematik, 101 (2013), 259-268.
75. Trudinger-Moser inequality with remainder terms, Journal of Functional Analysis, 266 (2014) 55-66.
76. (with David Costa) Concentration profiles for the Trudinger-Moser functional are shaped like toy pyramids, Journal of Functional Analysis 266 (2014), 676-692.
77. (with Jan Chabrowski) An elliptic problem with an indefinite nonlinearity and a parameter in the boundary condition, NoDEA Nonlinear Differential Equations Appl. 21 (2014), 519-540.
78. (with Ian Schindler) The limiting Dirac-Sobolev inequality, Rostok Math. Kolloquium 68 (2013), 3-12.
79. (with Adimurthi) On the Brezis-Lieb Lemma without pointwise convergence, NoDEA Nonlinear Differential Equations Appl. 22 (2015), 1515-1521.
80. (with Kanishka Perera) A nodal solution of the scalar field equation at the second minimax level, Bulletin of London Mathematical Society 46 (2014), 1218-1225.
81. (A) (with Sergio Solimini) On defect of compactness in Banach spaces, Comptes Rendus Acad. Sci. Paris 353 (2015), 899–903.
82. (S) (with Giuseppe Devillanova and Sergio Solimini) On weak convergence in metric spaces, Nonlinear Analysis and Optimization (B. S. Mordukhovich, S. Reich, A. J. Zaslavski, Editors), Contemporary Mathematics 659, Amer. Math. Soc., Providence, RI, 2016, pp. 43-63.
83. (with Sergio Solimini), Concentration analysis in Banach spaces, Communications in Contemporary Mathematics 18 (2016), 1550038 (33 pages).
84. (with Adimurthi) Defect of compactness in spaces of bounded variation, Journal of Functional Analysis 271 (2016), 37-48
85. (with Leszek Skrzypczak) On Caffarelli-Kohn-Nirenberg inequalities for block-radial functions, Potental Analisis, 45 (2016) 65-81. Online text: https://rdcu.be/7yaE
86. (with Kaniska Perera, Jun Wang and Zhitao Zhang) Ground and bound state solutions for a Schrödinger system with linear and nonlinear couplings in ℝ^N, Advances in Differential Equations 23 (2018), 615–648.
87. (with Arka Mallick) An improved Leray-Trudinger inequality, Communications in Contemporary Mathematics, online first - https://doi.org/10.1142/S0219199717500341
88. (S) Four proofs of cocompactness for Sobolev embeddings, in Functional Analysis, Harmonic Analysis and Image Processing: A collection of papers in honor of Björn Jawerth. Contemporary Mathematics 693, Amer. Math. Soc., Providence, RI, 2017, pp. 321-329.
89. (with Leszek Skrzypczak) Pointwise estimates for block-radial functions of Sobolev classes, Journal of Fourier Analysis and Applications, online first - https://doi.org/10.1007/s00041-018-9593-7
90. (with Kunnath Sandeep) A subset of Caffarelli-Kohn-Nirenberg inequalities in the hyperbolic space ℍ^N, Annali di Matematica Pura et Applicata, 196 (2017), 2005-2021.
91. (with Giuseppe Devillanova and Sergio Solimini) Profile decomposition in metric spaces, Pure and Applied Functional Analysis, 2, (2017), 625–654.
92. (with Ian Schindler) Compactness properties and ground states for the affine Laplacian, Calculus of Variations 2018 57:48 DOI: 10.1007/s00526-018-1338-6
93. (B) Concentration Compactness: Functional-analytic theory of concentration phenomena, 230pp., De Gruyter Series in Nonlinear Analysis and Applications 33, Walter de Gruyter GmbH, Berlin/Boston, ISBN 978-3-11-053043-2 (2020).
94. (with Leszek Skrzypczak) Defect of compactness for Sobolev spaces on manifolds with bounded geometry, Annali di Scuola Normale Superiore di Pisa, Cl. Sci (5), in press.
95. (P) (with G. Devillanova) A profile decomposition for the limiting Sobolev embedding, Proceedings of the Fifteenth International Conference Zaragoza-Pau on Mathematics and its Applications Jaca, 10-12 September 2018 (in press), Monografías Matemáticas García de Galdeano 42, 65–78 (2019)
96. (S+A) On defect of compactness in Sobolev embeddings on Riemannian manifolds, Algebra i Analiz 31, 36–54 (2019).
97. (with Ian Schindler) On compactness properties in the affine Sobolev inequality, Pure and Applied Functional Analysis, in press.
98. (with Kunnath Sandeep) Profile decomposition in Sobolev spaces of non-compact manifolds, NoDEA Nonlinear Differential Equations Appl. 26 (2019), no. 6, Paper No. 55.
99. (with Leszek Skrzypczak) On compact subsets of Sobolev spaces on manifolds, preprint.
100. (with Giuseppe Devillanova) Nonlinear Schrödinger equation with bounded magnetic field, Journal of Differential Equations 2020, https://doi.org/10.1016/j.jde.2020.06.010.
101. On compactness properties in Moser-Trudinger inequality for N-Laplacian, in preparation.
102. Nonlinear radial scalings and inequalities of Caffarelli-Kohn-Nirenberg type, in preparation.