A. A. Pankov, “On Nontrivial Solutions of a Nonlinear Schrödinger Equation with Magnetic Field”, Funktsional. Anal. i Prilozhen., 37:1 (2003), 88–91; Funct. Anal. Appl., 37:1 (2003), 75

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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 1, Pages 88–91
DOI: https://doi.org/10.4213/faa141 (Mi faa141)

This article is cited in 17 scientific papers (total in 17 papers)

Brief communications

On Nontrivial Solutions of a Nonlinear Schrödinger Equation with Magnetic Field

A. A. Pankov

Vinnitsa State Pedagogical University

Full-text PDF (112 kB) Citations (17)

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DOI: https://doi.org/10.4213/faa141

Abstract: We consider nonlinear magnetic Schrödinger equations under assumptions that imply the Palais–Smale condition for the corresponding functional and prove some results on the existence and multiplicity of solutions vanishing at infinity.

Keywords: nonlinear Schrödinger equation, Palais–Smale condition, multiplicity.

Received: 05.03.2002

English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 1, Pages 75–77
DOI: https://doi.org/10.1023/A:1022984313164

Bibliographic databases:

Document Type: Article

UDC: 517.97

Language: Russian

Citation: A. A. Pankov, “On Nontrivial Solutions of a Nonlinear Schrödinger Equation with Magnetic Field”, Funktsional. Anal. i Prilozhen., 37:1 (2003), 88–91; Funct. Anal. Appl., 37:1 (2003), 75–77

Citation in format AMSBIB

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https://doi.org/10.4213/faa141

https://www.mathnet.ru/eng/faa/v37/i1/p88

This publication is cited in the following 17 articles:

Wang D., “Concentration For a Biharmonic Schrodinger Equation”, Pac. J. Math., 289:2 (2017), 469–487
Guo Zh., Melgaard M., Zou W., “Schrodinger Equations With Magnetic Fields and Hardy-Sobolev Critical Exponents”, Electron. J. Differ. Equ., 2017, 199
Wang D., “Concentration For a Bi-Harmonic Schrodinger Equation With Critical Nonlinearity”, J. Math. Anal. Appl., 435:1 (2016), 380–401
Zhang W., Tang X., Zhang J., “Multiple Solutions For Semilinear Schrodinger Equations With Electromagnetic Potential”, Electron. J. Differ. Equ., 2016, 26
Zhang J., Tang X., Zhang W., “Semiclassical Solutions For a Class of Schrodinger System With Magnetic Potentials”, J. Math. Anal. Appl., 414:1 (2014), 357–371
Ding Ya., Liu X., “Semiclassical Solutions of Schrodinger Equations with Magnetic Fields and Critical Nonlinearities”, Manuscr. Math., 140:1-2 (2013), 51–82
Zhang G., “Breather solutions of the discrete nonlinear Schrodinger equations with sign changing nonlinearity”, J Math Phys, 52:4 (2011), 043516
Abatangelo L., Terracini S., “Solutions to nonlinear Schrodinger equations with singular electromagnetic potential and critical exponent”, J Fixed Point Theory Appl, 10:1 (2011), 147–180
Ding Ya., Wang Zh.-Q., “Bound states of nonlinear Schrodinger equations with magnetic fields”, Ann Mat Pura Appl, 190:3 (2011), 427–451
Clapp M., Szulkin A., “Multiple solutions to a nonlinear Schrodinger equation with Aharonov-Bohm magnetic potential”, Nodea-Nonlinear Differential Equations and Applications, 17:2 (2010), 229–248
Zhang G., Pankov A., “Standing wave solutions of the discrete non-linear Schrodinger equations with unbounded potentials, II”, Appl Anal, 89:9 (2010), 1541–1557
Cingolani S., Clapp M., “Symmetric Semiclassical States To a Magnetic Nonlinear Schrodinger Equation Via Equivariant Morse Theory”, Commun Pure Appl Anal, 9:5 (2010), 1263–1281
Clapp, M, “Periodic and Bloch Solutions to a Magnetic Nonlinear Schrodinger Equation”, Advanced Nonlinear Studies, 9:4 (2009), 639
Cingolani, S, “Intertwining semiclassical bound states to a nonlinear magnetic Schrodinger equation”, Nonlinearity, 22:9 (2009), 2309
Zhang, GP, “Breather solutions of the discrete nonlinear Schrodinger equations with unbounded potentials”, Journal of Mathematical Physics, 50:1 (2009), 013505
Wang, FZ, “On an electromagnetic Schrodinger equation with critical growth”, Nonlinear Analysis-Theory Methods & Applications, 69:11 (2008), 4088
Chabrowski J., Szulkin A., “On the Schrödinger equation involving a critical Sobolev exponent and magnetic field”, Topol. Methods Nonlinear Anal., 25:1 (2005), 3–21

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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