International Journal of Nonlinear Analysis and Applications

On a class of Schrodinger-Kirchhoff-Poisson systems

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

2 Department of Mathematics, Faculty of Basic Science, Babol Noshirvani University of Technology, Babol, Iran

10.22075/ijnaa.2024.35087.5241

Abstract

This article discusses the existence and multiplicity of solutions for ‎‎‎the following‎ ‎Schrodinger-Kirchhoff-Poisson ‎system:‎
‎‎‎{‎‎‎−‎(a+b∫R3|∇u|2)‎‎Δ‎u‎+‎λϕu=m(x)|u|q−2u‎+‎f(x,u)‎,‎x∈‎Ω‎,‎‎‎‎‎‎−‎Δ‎ϕ=u2, ‎ ‎‎ ‎x∈‎Ω‎,‎‎‎‎‎
‎where ‎‎Ω‎ ‎is a‎ ‎bounded ‎smooth ‎domain ‎of‎ ‎‎‎‎R‎3‎,‎ a≥0‎ ,‎b>0 and λ>0 is a ‎parameter,‎‎ ‎1<q<2 and f(x,u) is linearly bounded in u at infinity‎. ‎Under some suitable‎ ‎assumptions on m and f‎,‎ we prove the existence and multiplicity of solutions via variational methods.‎

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 05 April 2025
  • Receive Date: 14 August 2024
  • Accept Date: 18 September 2024