全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

Ground State Solutions for the Fractional Klein-Gordon-Maxwell System with Steep Potential Well

DOI: 10.4236/oalib.1109189, PP. 1-15

Subject Areas: Partial Differential Equation

Keywords: Fractional Laplacian, Klein-Gordon-Maxwell System, Ground state Solution, Steep Potential Well, Variational Methods

Full-Text   Cite this paper   Add to My Lib

Abstract

In this paper, we study the fractional Klein-Gordon-Maxwell system with steep potential well. On the basis of overcoming the lack of compactness, the ground state solution is obtained by proving that the solution satisfies the mountain pass level.

Cite this paper

Shi, Q. (2022). Ground State Solutions for the Fractional Klein-Gordon-Maxwell System with Steep Potential Well. Open Access Library Journal, 9, e9189. doi: http://dx.doi.org/10.4236/oalib.1109189.

References

[1]  Di Nezza, E., Palatucci, G. and Valdinoci, E. (2012) Hitchhiker's Guide to the Fractional Sobolev Spaces. Bulletin des sciences mathématiques, 136, 521-573. https://doi.org/10.1016/j.bulsci.2011.12.004
[2]  Barrios, B., Colorado, E., De Pablo, A. and Sánchez. U. (2012) On Some Critical Problems for the Fractional Laplacian Operator. Journal of Differential Equations, 252, 6133-6162. https://doi.org/10.1016/j.jde.2012.02.023
[3]  Caffarelli, L. and Silvestre, L. (2007) An Extension Problem Related to the Fractional Laplacian. Communications in Partial Differential Equations, 32, 1245-1260. https://doi.org/10.1080/03605300600987306
[4]  Chang, X.J. and Wang, Z.Q. (2013) Ground State of Scalar Field Equations Involving a Fractional Laplacian with General Nonlinearity. Nonlinearity, 26, 479-494. https://doi.org/10.1088/0951-7715/26/2/479
[5]  Miyagaki, O.H., de Moura, E.L. and Ruviaro, R. (2019) Positive Ground State Solutions for Quasicritical the Fractional Klein-Gordon-Maxwell System with Potential Vanishing at Infinity. Complex Variables and Elliptic Equations, 64, 315-329. https://doi.org/10.1080/17476933.2018.1434625
[6]  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
[7]  Carriao, P.C., Cunha, P.L. and Miyagaki, O.H. (2012) Positive Ground State Solutions for the Klein-Gordon-Maxwell System with Potentials. Nonlinear Analysis: Theory, Methods & Applications, 75, 4068-4078. https://doi.org/10.1016/j.na.2012.02.023
[8]  Chen, S.T. and Tang, X.H. (2018) Infinitely Many Solutions and Least Energy Solutions for Klein-Gordon-Maxwell Systems with General Superlinear Nonlinearity. Computers & Mathematics with Applications, 75, 3358-3366. https://doi.org/10.1016/j.camwa.2018.02.004
[9]  Cunha, P.L. (2014) Subcritical and Supercritical Klein-Gordon-Maxwell Equations without Ambrosetti-Rabinowitz Condition. Differential and Integral Equations, 27, 387-399.
[10]  Leal de Moura, E., Hiroshi Miyagaki, O. and Ruviaro, R. (2017) Positive Ground State Solutions for Quasicritical Klein-Gordon-Maxwell Type Systems with Potential Vanishing at Infinity. Electronic Journal of Differential Equations, 2017, 1-11.
[11]  Liu, X.Q., Chen, S.J. and Tang, C.L. (2019) Ground State Solutions for Klein-Gordon-Maxwell System with Steep Potential Well. Applied Mathematics Letters, 90, 175-180. https://doi.org/10.1016/j.aml.2018.11.002
[12]  Zhang, Q.F., Gan, C.L., Xiao, T. and Jia, Z. (2020) An Improved Result for Klein-Gordon-Maxwell Systems with Steep Potential Well. Mathematical Methods in the Applied Sciences, 44, 11856-11862. https://doi.org/10.1002/mma.6514
[13]  D’Aprile, T. and Mugnai, D. (2004) Non-Existence Results for the Coupled Klein-Gordon-Maxwell Equations. Advanced Nonlinear Studies, 4, 307-322. https://doi.org/10.1515/ans-2004-0305
[14]  D’Aprile, T. and Mugnai, D. (2004) Solitary Waves for Nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell Equations. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 134, 893-906. https://doi.org/10.1017/S030821050000353X
[15]  Bartsch, T. and Wang, Z. Q. (1995) Existence and Multiplicity Results for Some Superlinear Elliptic Problems on : Existence and Multiplicity Results. Communications in Partial Differential Equations, 20, 1725-1741. https://doi.org/10.1080/03605309508821149
[16]  Brändle, C., Colorado, E., de Pablo, A. and Sánchez, U. (2013) A Concave-Convex Elliptic Problem Involving the Fractional Laplacian. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 143, 39-71. https://doi.org/10.1017/S0308210511000175
[17]  Zhang, J. (2017) Solutions to the Critical Klein-Gordon-Maxwell System with External Potential. Journal of Mathematical Analysis and Applications, 455, 1152-1177. https://doi.org/10.1016/j.jmaa.2017.06.028

Full-Text


comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133

WeChat 1538708413