带有位势的Schrödinger-Poisson系统解的存在性与多解性

Abstract

Abstract:

In this paper, we discuss the existence and multiplicity solutions to the following Schrödinger-Poisson system with potentials
-Δu+λVu+φu=f(x,u),x∈R³
-Δφ=u²,x∈R³
where λ≥qslant1 is a parameter, the potential V∈C(R³, R₊) and satisfies the more general assumptions. When f is 4-superlinear at infinity, we discuss the existence and multiplicity of solutions for λ≥1 large enough without the compactness of embedding of the work space. We also consider the existence of infinity many solutions with f satisfying the more general sublinear assumptions.

Key words: Schrödinger-Poisson system, Potential, Variational method, 4-Superlinear, Sublinear

CLC Number:

O175.29

Zhang Qi. Existence and Multiplicity of Solutions to Schrödinger-Poisson System with Potentials[J].Acta mathematica scientia,Series A, 2016, 36(1): 49-64.

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Existence and Multiplicity of Solutions to Schrödinger-Poisson System with Potentials

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