Existence of infinitely many solutions to a class of Kirchhoff–Schrödinger–Poisson system

Guilan Zhao, Xiaoli Zhu and Yuhua Li

Applied Mathematics and Computation, 2015, vol. 256, issue C, 572-581

Abstract: In this paper, we consider the existence of infinitely many solutions to following nonlinear Kirchhoff–Schrödinger–Poisson systema+b∫R3|∇u|2+V(x)u2-Δu+V(x)u+λl(x)ϕu=f(x,u),x∈R3,-Δϕ=λl(x)u2,x∈R3,where constants a>0,b⩾0 and λ⩾0. When f has sublinear growth in u, we obtain infinitely many solutions under certain assumption that V do not have a positive lower bound. The technique we use in this paper is the symmetric mountain pass theorem established by Kajikiya (2005).

Keywords: Kirchhoff–Schrödinger–Poisson system; Sublinear; Variational method; Symmetric mountain pass theorem (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:256:y:2015:i:c:p:572-581

DOI: 10.1016/j.amc.2015.01.038

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