[27] R. Adami, F. Boni, R. Carlone, L. Tentarelli, The search for NLS ground states on a hybrid domain: Motivations, methods, and results, preprint, arXiv:2404.07843 [math.AP] (2024). Contribution for the Proceedings of the Summer School of the Puglia Trimester 2023 “Singularities, Asymptotics and Limiting Models”.

Link: arXiv 

[25] D. Finco, L. Tentarelli, A. Teta, Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity, Nonlinearity 37 (2024), no. 1, article number 015009, 48pp. Doi=10.1088/1361-6544/ad0aac, Scopus=2-s2.0-85180101020, Wos=WOS:001119846100001, Msn=MR4679004.

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[24] L. Tentarelli, A general review on the NLS equation with point-concentrated nonlinearity, Commun. Appl. Ind. Math. 14 (2023), no. 1, 62-84. Doi=10.2478/caim-2023-0004, Scopus=2-s2.0-85175313113, Wos=WOS:001086921200001, Msn=MR4653819.

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[23] W. Borrelli, R. Carlone, L. Tentarelli, Complete ionization for a non-autonomous point interaction model in d = 2, Comm. Math. Phys. 395 (2022), no. 2, 963-1005. Doi=10.1007/s00220-022-04447-1, Scopus=2-s2.0-85133587861, Wos=WOS:000825003000001, Msn=MR4487529.

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[22] R. Adami, F. Boni, R. Carlone, L. Tentarelli, Ground states for the planar NLSE with a point defect as minimizers of the constrained energy, Calc. Var. Partial Differential Equations 61 (2022), no. 5, article number 195, 32pp. Doi=10.1007/s00526-022-02310-8, Scopus=2-s2.0-85136057007, Wos=WOS:000840855300001, Msn=MR4469484.

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[21] R. Adami, F. Boni, R. Carlone, L. Tentarelli, Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect, J. Math. Phys. 63 (2022), no. 7, article number 071501, 16pp. Special Collection on the Proceedings of ICMP XX . Doi=10.1063/5.0091334, Scopus=2-s2.0-85133696386, Wos=WOS:000933413200002, Msn=MR4446510.

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[20] S. Dovetta, L. Tentarelli, Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover, J. Math. Pures Appl. (9) 160 (2022), 99-157. Doi=10.1016/j.matpur.2021.12.010, Scopus=2-s2.0-85122796767, Wos=WOS:000766609200004, Msn=MR4389759.

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[19] W. Borrelli, R.Carlone, L. Tentarelli, A note on the Dirac operator with Kirchoff-type vertex conditions on noncompact metric graphs, Springer INdAM Series 42 (2021), 81-104. Volume “Mathematical Challenges of Zero-Range Physics”. Doi=10.1007/978-3-030-60453-0_4, Scopus=2-s2.0-85099305609, Msn=MR4219183.

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[18] W. Borrelli, R.Carlone, L. Tentarelli, On the nonlinear Dirac equation on noncompact metric graphs, J. Differential Equations 278 (2021), 326-357. Doi=10.1016/j.jde.2021.01.005, Scopus=2-s2.0-85099305609, Wos=WOS:000613291600011, Msn=MR4200758.

Link: publisher, arXiv

[17] R. Adami, R. Carlone, M. Correggi, L. Tentarelli, Stability of the standing waves of the concentrated NLSE in dimension two, Mathematics in Engineering 3 (2021), no. 2, 1-15. Special Issue “Nonlinear models in applied mathematics”. Doi=10.3934/mine.2021011, Wos=WOS:000623147100001, Msn=MR4146039.

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[16] S. Dovetta, L. Tentarelli, Ground states of the L^2-critical NLS equation with localized nonlinearity on a tadpole graph, Oper. Theory Adv. Appl. 281 (2020), 113-125. Volume “Discrete and Continuous Models in the Theory of Networks”. Doi=10.1007/978-3-030-44097-8_5, Scopus=2-s2.0-85091062465.

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[15] R. Adami, R.Carlone, M. Correggi, L. Tentarelli, Blow-up for the pointwise NLS in dimension two: absence of critical power, J. Differential Equations 269 (2020), no. 1, 1-37. Doi=10.1016/j.jde.2019.11.096, Scopus=2-s2.0-85076245658, Wos=WOS:000523564600001, Msn=MR4081515.

Links: publisher, arXiv

[14] R.Carlone, D. Finco, L. Tentarelli, Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one,  Nonlinearity 32 (2019), no. 8, 3112-3143. Doi=10.1088/1361-6544/ab1273, Scopus=2-s2.0-85071659993, Wos=WOS:000476588900011, Msn=MR3987813.

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[13] S. Dovetta, L. Tentarelli, L^2-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features, Calc. Var. Partial Differential Equations 58 (2019), no. 3, article number 108, 26pp. Doi=10.1007/s00526-019-1565-5, Scopus=2-s2.0-85067016339, Wos=WOS:000470669300003, Msn=MR3959930.

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[12] W. Borrelli, R.Carlone, L. Tentarelli, Nonlinear Dirac equation on graphs with localized nonlinearities: bound states and nonrelativistic limit, SIAM J. Math. Anal. 51 (2019), no. 2, 1046-1081. Doi=10.1137/18M1211714, Scopus=2-s2.0-85065479380, Wos=WOS:000464913300015, Msn=MR3934110.

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[11] L. Tentarelli, P. Tilli, An existence result for dissipative nonhomogeneous hyperbolic equations via a minimization approach,  J. Differential Equations 266 (2019), no. 8, 5185-5208. Doi=10.1016/j.jde.2018.10.023, Scopus=2-s2.0-85055487375, Wos=WOS:000457739900023, Msn=MR3912746.

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[10] W. Borrelli, R. Carlone, L. Tentarelli, An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity,  Symmetry 11 (2019), no. 2, article number 169, 22pp. Special Issue “Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks”. Doi=10.3390/sym11020169, Scopus=2-s2.0-85061849048,  Wos=WOS:000460767300047.

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[9] R. Carlone, M. Correggi, L. Tentarelli, Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 1,  257-294.  Doi=10.1016/j.anihpc.2018.05.003, Scopus=2-s2.0-85048193951, Wos=WOS:000456754200010, Msn=MR3906872.

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[8] L. Tentarelli, P. Tilli, De Giorgi’s approach to hyperbolic Cauchy problems: the case of nonhomogeneous equations, Comm. Partial Differential Equations 43 (2018), no. 4. 677-698. Doi=10.1080/03605302.2018.1459686, Scopus=2-s2.0-85045749008, Wos=WOS:000457052900006, Msn=MR3902175.

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[7] R. Carlone, M. Correggi, L. Tentarelli, An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions, Nanosystems: Phys. Chem. Math. 9 (2018), no. 2, 187-195. Doi=10.17586/2220-8054-2018-9-2-187-195, Wos=WOS:000431269000005.

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[6] R. Carlone, R. Figari, C. Negulescu, L. Tentarelli, Solvable models of quantum beating, Nanosystems: Phys. Chem. Math. 9 (2018), no. 2, 162-170. Doi=10.17586/2220-8054-2018-9-2-162-170, Wos=WOS:000431269000002.

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[5] R. Carlone, A. Fiorenza, L. Tentarelli, The action of Volterra integral operators with highly singular kernels on Hölder continuous, Lebesgue and Sobolev functions, J. Funct. Anal. 273 (2017), no. 3, 1258-1294. Doi=10.1016/j.jfa.2017.04.013, Scopus=2-s2.0-85019022970, Wos=WOS:000402852300012, Msn=MR3653953.

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[4] L. Tentarelli, On the extensions of the De Giorgi approach to nonlinear hyperbolic equations, Rend. Semin. Mat. Univ. Politec. Torino 74 (2016), no. 3-4, 151-160. Special Issue for the conference “Bruxelles-Turin talks in PDE’s” held in Turin, May 2-5, 2016. Scopus=2-s2.0-85043599533, Msn=MR3772608.

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[3] E. Serra, L. Tentarelli, On the lack of bound states for certain NLS equations on metric graphs, Nonlinear Anal. 145 (2016), 68-82. Doi=10.1016/j.na.2016.07.008, Scopus=2-s2.0-84981295044, Wos=WOS:000384850700004, Msn=MR3547674.

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[2] E. Serra, L. Tentarelli, Bound states of the NLS equation on metric graphs with localized nonlinearities, J. Differential Equations 260 (2016), no. 7, 5627-5644. Doi=10.1016/j.jde.2015.12.030, Scopus=2-s2.0-84958105709, Wos=WOS:000374510900004, Msn=MR3456809.

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