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Normalized Solutions of Mass-Subcritical Klein-Gordon-Maxwell Systems

DOI: 10.4236/oalib.1110464, PP. 1-9

Subject Areas: Mathematics

Keywords: Normalized Solutions, Klein-Gordon-Maxwell Systems

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Abstract

In this paper, we study the existence of normalized solutions to the Klein-Gordon-Maxwell systems. In the mass-subcritical case, we prove that the systems satisfying normalization conditions have a normalized ground state solution.

Cite this paper

Wang, Z. (2023). Normalized Solutions of Mass-Subcritical Klein-Gordon-Maxwell Systems. Open Access Library Journal, 10, e464. doi: http://dx.doi.org/10.4236/oalib.1110464.

References

[1]  Carrião, P.C., Cunha, P.L. and Miyagaki, O.H. (2012) Positive Ground State Solutions for the Critical Klein-Gordon-Maxwell System with Potentials. Nonlinear Analysis: Theory, Methods & Applications, 75, 4068-4078. https://doi.org/10.1016/j.na.2012.02.023
[2]  Zhang, X. and Huang, C. (2022) Nontrivial Solutions for Klein-Gordon-Maxwell Systems with Sign-Changing Potentials. Boundary Value Problems, 10, Article No. 83. https://doi.org/10.1186/s13661-022-01664-4
[3]  Cassani, D. (2004) Existence and Non-Existence of Solitary Waves for the Critical Klein-Gordon Equation Coupled with Maxwell’s Equations. Nonlinear Analysis: Theory, Methods & Applications, 58, 733-747. https://doi.org/10.1016/j.na.2003.05.001
[4]  Benci, V. and Fortunato, D. (2002) Solitary Waves of the Nonlinear Klein-Gordon Equation Coupled with the Maxwell Equations. Reviews in Mathematical Physics, 14, 409-420. https://doi.org/10.1142/S0129055X02001168
[5]  He, C.-M., Li, L., Chen, S.-J. and O’Regan, D. (2022) Ground State Solution for the Nonlinear Klein-Gordon Equation Coupled with Born-Infeld Theory with Critical Exponents. Analysis and Mathematical Physics, 12, Article No. 48. https://doi.org/10.1007/s13324-022-00661-1
[6]  Wang, F. (2011) Ground-State Solutions for the Electrostatic Nonlinear Klein-Gordon-Maxwell System. Nonlinear Analysis: Theory, Methods & Applications, 74, 4796-4803. https://doi.org/10.1016/j.na.2011.04.050
[7]  Wang, F. (2011) Solitary Waves for the Klein-Gordon-Maxwell System with Critical Exponent. Nonlinear Analysis: Theory, Methods & Applications, 74, 827-835. https://doi.org/10.1016/j.na.2010.09.033
[8]  Bartsch, T. and Jeanjean, L. (2018) Normalized Solutions for Nonlinear Schrödinger Systems. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 148, 225-242. https://doi.org/10.1017/S0308210517000087
[9]  Bartsch, T., Jeanjean, L. and Soave, N. (2016) Normalized Solutions for a System of Coupled Cubic Schrödinger Equations on . Journal de Mathématiques Pures et Appliquées, 106, 583-614. https://doi.org/10.1016/j.matpur.2016.03.004
[10]  Bartsch, T. and Soave, N. (2017) A Natural Constraint Approach to Normalized Solutions of Nonlinear Schrödinger Equations and Systems. Journal of Functional Analysis, 272, 4998-5037. https://doi.org/10.1016/j.jfa.2017.01.025
[11]  Bartsch, T. and Soave, N. (2019) Multiple Normalized Solutions for a Competing System of Schrödinger Equations. Calculus of Variations and Partial Differential Equations, 58, Article No. 22. https://doi.org/10.1007/s00526-018-1476-x
[12]  Gou, T. and Jeanjean, L. (2018) Multiple Positive Normalized Solutions for Nonlinear Schrödinger Systems. Nonlinearity, 31, 2319-2345. https://doi.org/10.1088/1361-6544/aab0bf
[13]  Ikoma, N. and Tanaka, K. (2019) A Note on Deformation Argument for Normalized Solutions of Nonlinear Schrödinger Equations and Systems. Advances in Differential Equations, 24, 609-646. https://doi.org/10.57262/ade/1571731543
[14]  Yang, Z., Qi, S. and Zou, W. (2022) Normalized Solutions of Nonlinear Schrödinger Equations with Potentials and Non-Autonomous Nonlinearities. Journal of Geometric Analysis, 32, Article No. 159. https://doi.org/10.1007/s12220-022-00897-0
[15]  Soave, N. (2020) Normalized Ground States for the NLS Equation with Combined Nonlinearities: The Sobolev Critical Case. Journal of Functional Analysis, 279, Article ID: 108610. https://doi.org/10.1016/j.jfa.2020.108610
[16]  Shibata, M. (2014) Stable Standing Waves of Nonlinear Schrödinger Equations with a General Nonlinear Term. Manuscripta Mathematica, 143, 221-237. https://doi.org/10.1007/s00229-013-0627-9
[17]  Ikoma, N. and Miyamoto, Y. (2020) Stable Standing Waves of Nonlinear Schrödinger Equations with Potentials and General Nonlinearities. Calculus of Variations and Partial Differential Equations, 59, Article No. 48. https://doi.org/10.1007/s00526-020-1703-0
[18]  Chen, Z. and Zou, W. (2021) Normalized Solutions for Nonlinear Schrödinger Systems with Linear Couples. Journal of Mathematical Analysis and Applications, 499, Article ID: 125013. https://doi.org/10.1016/j.jmaa.2021.125013
[19]  Bartsch, T., Molle, R., Rizzi, M. and Verzini, G. (2021) Normalized Solutions of Mass Supercritical Schrödinger Equations with Potential. Communications in Partial Differential Equations, 46, 1729-1756. https://doi.org/10.1080/03605302.2021.1893747
[20]  Bartsch, T. and de Valeriola, S. (2013) Normalized Solutions of Nonlinear Schrödinger Equations. Archiv der Mathematik, 100, 75-83. https://doi.org/10.1007/s00013-012-0468-x
[21]  Zhu, X. and Cao, D. (1989) The Concentration-Compactness Principle in Nonlinear Elliptic Equations. Acta Mathematica Scientia, 9, 307-328. https://doi.org/10.1016/S0252-9602(18)30356-4
[22]  Zou, W. and Schechter, M. (2006) Critical Point Theory and Its Applications. Springer, New York.

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