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

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...

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Bibliographic Details
Published in:Applied mathematics and computation 2015-04, Vol.256, p.572-581
Main Authors: Zhao, Guilan, Zhu, Xiaoli, Li, Yuhua
Format: Article
Language:English
Subjects:
Kirchhoff–Schrödinger–Poisson system
Sublinear
Symmetric mountain pass theorem
Variational method
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Summary: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).
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2015.01.038