Comptes Rendus
no. 1
Partial differential equations
Multiplicity for a 4-sublinear Schrödinger–Poisson system with sign-changing potential via Morse theory

Présenté par : the Editorial Board

Hongliang Liu1 ; Haibo Chen1 ; Gangwei Wang2, 3
1 School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, PR China
2 Department of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada
3 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China
Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 75-80.

In this paper, we study a 4-sublinear Schrödinger–Poisson system with sign-changing potential. Under some suitable assumptions, the existence of two nontrivial solutions are obtained by using the Morse theory. Our result improves the recent ones of Chen and Zhang (2014) [6].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.10.018
Mots-clés : Schrödinger–Poisson system, Morse theory, Critical groups, Sign-changing potential

Hongliang Liu 1 ; Haibo Chen 1 ; Gangwei Wang 2, 3

1 School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, PR China
2 Department of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada
3 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China 
@article{CRMATH_2016__354_1_75_0,
     author = {Hongliang Liu and Haibo Chen and Gangwei Wang},
     title = {Multiplicity for a 4-sublinear {Schr\"odinger{\textendash}Poisson} system with sign-changing potential via {Morse} theory},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {75--80},
     publisher = {Elsevier},
     volume = {354},
     number = {1},
     year = {2016},
     doi = {10.1016/j.crma.2015.10.018},
     language = {en},
}
TY  - JOUR
AU  - Hongliang Liu
AU  - Haibo Chen
AU  - Gangwei Wang
TI  - Multiplicity for a 4-sublinear Schrödinger–Poisson system with sign-changing potential via Morse theory
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 75
EP  - 80
VL  - 354
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2015.10.018
LA  - en
ID  - CRMATH_2016__354_1_75_0
ER  - 
%0 Journal Article
%A Hongliang Liu
%A Haibo Chen
%A Gangwei Wang
%T Multiplicity for a 4-sublinear Schrödinger–Poisson system with sign-changing potential via Morse theory
%J Comptes Rendus. Mathématique
%D 2016
%P 75-80
%V 354
%N 1
%I Elsevier
%R 10.1016/j.crma.2015.10.018
%G en
%F CRMATH_2016__354_1_75_0
Hongliang Liu; Haibo Chen; Gangwei Wang. Multiplicity for a 4-sublinear Schrödinger–Poisson system with sign-changing potential via Morse theory. Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 75-80. doi : 10.1016/j.crma.2015.10.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.018/

[1] S. Alama; G. Tarantello On semilinear elliptic equations with indefinite nonlinearities, Calc. Var. Partial Differ. Equ., Volume 1 (1993), pp. 439-475

[2] G. Cerami; G. Vaira Positive solutions for some non-autonomous Schrödinger–Poisson systems, J. Differ. Equ., Volume 248 (2010), pp. 521-543

[3] K. Chang Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, Basel, Berlin, 1993

[4] J. Chen Multiple positive solutions of a class of non autonomous Schrödinger–Poisson systems, Nonlinear Anal., Real World Appl., Volume 21 (2015), pp. 13-26

[5] P. Chen; C. Tian Infinitely many solutions for Schrödinger–Maxwell equations with indefinite sign subquadratic potentials, Appl. Math. Comput., Volume 226 (2014), pp. 492-502

[6] S. Chen; D. Zhang Existence of nontrivial solution for a 4-sublinear Schrödinger–Poisson system, Appl. Math. Lett., Volume 38 (2014), pp. 135-139

[7] W. Huang; X. Tang Semiclassical solutions for the nonlinear Schrödinger–Maxwell equations, J. Math. Anal. Appl., Volume 415 (2014), pp. 791-802

[8] W. Huang; X. Tang The existence of infinitely many solutions for the nonlinear Schrödinger–Maxwell equations, Results Math., Volume 65 (2014), pp. 223-234

[9] L. Huang; E.M. Rocha; J. Chen Two positive solutions of a class of Schrödinger–Poisson system with indefinite nonlinearity, J. Differ. Equ., Volume 255 (2013), pp. 2463-2483

[10] Y. Jiang; H. Zhou Schrödinger–Poisson system with steep potential well, J. Differ. Equ., Volume 251 (2011), pp. 582-608

[11] Y. Jiang; H. Zhou Schrödinger–Poisson system with singular potential, J. Math. Anal. Appl., Volume 417 (2014), pp. 411-438

[12] H. Liu; H. Chen; X. Yang Multiple solutions for superlinear Schrödinger–Poisson system with sign-changing potential and nonlinearity, Comput. Math. Appl., Volume 68 (2014), pp. 1982-1990

[13] Z. Liu; S. Guo; Z. Zhang Existence of ground state solutions for the Schrödinger–Poisson systems, Appl. Math. Comput., Volume 244 (2014), pp. 312-323

[14] J. Mawhin; M. Willem Critical Point Theory and Hamiltonian Systems, Springer, Berlin, 1989

[15] M. Reed; B. Simon Methods of Modern Mathematical Physics, IV: Analysis of Operators, Academic Press, New York, London, 1978

[16] D. Ruiz The Schrödinger–Poisson equation under the effect of a nonlinear local term, J. Funct. Anal., Volume 237 (2006), pp. 655-674

[17] J. Sun; H. Chen; L. Yang Positive solutions of asymptotically linear Schrödinger–Poisson systems with a radial potential vanishing at infinity, Nonlinear Anal., Volume 74 (2011), pp. 413-423

[18] J. Sun; H. Chen; J.J. Nieto On ground state solutions for some non autonomous Schrödinger–Poisson systems, J. Differ. Equ., Volume 252 (2012), pp. 3365-3380

[19] L. Xu; H. Chen Multiplicity of small negative-energy solutions for a class of nonlinear Schrödinger–Poisson systems, Appl. Math. Comput., Volume 243 (2014), pp. 817-824

[20] L. Xu; H. Chen Existence of infinitely many solutions for generalized Schrödinger–Poisson system, Bound. Value Probl., Volume 2014 (2014)

[21] M. Yang; Z. Han Existence and multiplicity results of the nonlinear Schrödinger–Poisson systems, Nonlinear Anal., Real World Appl., Volume 13 (2012), pp. 1093-1101

  • Guofeng Che; Haibo Chen Existence and multiplicity of solutions for Kirchhoff–Schrödinger–Poisson system with critical growth, International Journal of Mathematics, Volume 33 (2022) no. 01 | DOI:10.1142/s0129167x22500082
  • Sofiane Khoutir LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR SUPER-QUADRATIC SCHRÖDINGER-POISSON SYSTEMS IN R3, Journal of Applied Analysis Computation, Volume 11 (2021) no. 3, p. 1520 | DOI:10.11948/20200274
  • Jie Yang; Haibo Chen; Senli Liu The existence of nontrivial solution of a class of Schrödinger–Bopp–Podolsky system with critical growth, Boundary Value Problems, Volume 2020 (2020) no. 1 | DOI:10.1186/s13661-020-01442-0
  • Belal Almuaalemi; Haibo Chen; Sofiane Khoutir Existence of Nontrivial Solutions for Schrödinger–Poisson Systems with Critical Exponent on Bounded Domains, Bulletin of the Malaysian Mathematical Sciences Society, Volume 42 (2019) no. 4, p. 1675 | DOI:10.1007/s40840-017-0570-0
  • Sofiane Khoutir; Haibo Chen Positive ground state solutions for a class of Schrödinger–Poisson systems in R4 involving critical Sobolev exponent, Asymptotic Analysis, Volume 109 (2018) no. 1-2, p. 91 | DOI:10.3233/asy-181471
  • Belal Almuaalemi; Haibo Chen; Sofiane Khoutir Existence and multiplicity of nontrivial solutions for Schrödinger-Poisson systems on bounded domains, Boundary Value Problems, Volume 2018 (2018) no. 1 | DOI:10.1186/s13661-018-0933-y
  • Alex M. Batista; Marcelo F. Furtado Positive and nodal solutions for a nonlinear Schrödinger–Poisson system with sign-changing potentials, Nonlinear Analysis: Real World Applications, Volume 39 (2018), p. 142 | DOI:10.1016/j.nonrwa.2017.06.005
  • Xiaonan Liu; Haibo Chen Positive solutions for a class of quasilinear Schrödinger equations with vanishing potentials, Boundary Value Problems, Volume 2017 (2017) no. 1 | DOI:10.1186/s13661-017-0769-x
  • Hongliang Liu; Haibo Chen; Qizhen Xiao Positive ground state solutions for a class of Schrödinger–Poisson systems with sign‐changing and vanishing potential, Mathematical Methods in the Applied Sciences, Volume 40 (2017) no. 6, p. 1937 | DOI:10.1002/mma.4110
  • Hongliang Liu; Haibo Chen Multiple solutions for a nonlinear Schrödinger–Poisson system with sign-changing potential, Computers Mathematics with Applications, Volume 71 (2016) no. 7, p. 1405 | DOI:10.1016/j.camwa.2016.02.010

Cité par 10 documents. Sources : Crossref

☆ Research supported by Hunan Provincial Foundation For Postgraduate CX2014B044, National Natural Science Foundation of China 11271372 and Hunan Provincial Natural Science Foundation of China 12JJ2004.

Commentaires - Politique