临界情形下Schrödinger-Maxwell方程的基态解

Abstract

Abstract:

In this paper, we study the existence of the ground state solutions for the following Schrödinger-Maxwell equations

$\left\{\begin{array}{ll} -\triangle u+V(x)u-(K(x)+\alpha)\phi u=\beta|u|^{4}u+b(x)|u|^{p-1}u, &(x,u)\in(\mathbb{R}^{3},\mathbb{R}),\\ \triangle\phi=(K(x)+\alpha)u^{2},& (x,u)\in(\mathbb{R}^{3},\mathbb{R}) \end{array} \right.$

where β is a positive constant. Under some assumptions on V, K and b(x), by using the variational method and critical point theorem, we prove that such a class of equations has at least a ground state solution for α < 0 and p ∈ (3, 4).

Key words: Schrödinger-Maxwell equations, Critical point theorem, Critical growth, Ground state solution, Nehari manifold

CLC Number:

O175.25

Liwan Fang,Wennian Huang,Minqing Wang. Ground-State Solutions for Schrödinger-Maxwell Equations in the Critical Growth[J].Acta mathematica scientia,Series A, 2019, 39(3): 475-483.

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References

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Ground-State Solutions for Schrödinger-Maxwell Equations in the Critical Growth

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