一类次线性Schrödinger-Maxwell方程无穷多非平凡解的存在性

The Existence of Infinitely Many Nontrivial Solutions for a Kind of Schrödinger-Maxwell Equation with Sublinear Potentials

摘要: 本文借助变分法和临界点理论研究一类次线性Schrödinger-Maxwell方程无穷多非平凡解的存在性问题$\{\begin{array}{ll}-\Delta u+V\left(x\right)u+\alpha \varphi f\left(u\right)=g\left(x,u\right),\hfill & x\in {\text{R}}^3,\hfill \\ -\Delta \varphi =2\alpha F\left(u\right),\hfill & x\in {\text{R}}^3.\hfill \end{array}$ 其中$\alpha >0$ ，$V\left(x\right)\in C^1\left({\text{R}}^3,\text{R}\right)$ ，$V\left(x\right)>0$ 。在$f,g$ 符合相关条件下，$p\in \left(1,2\right)$ 。

Abstract: In this paper, we discuss the existence of infinitely many nontrivial solutions for the following kind of sublinear Schrödinger-Maxwell equation by using the variational method and critical point theory. $\{\begin{array}{ll}-\Delta u+V\left(x\right)u+\alpha \varphi f\left(u\right)=g\left(x,u\right),\hfill & x\in {\text{R}}^3,\hfill \\ -\Delta \varphi =2\alpha F\left(u\right),\hfill & x\in {\text{R}}^3.\hfill \end{array}$ where $\alpha >0$ , $V\left(x\right)\in C^1\left({\text{R}}^3,\text{R}\right)$ , $V\left(x\right)>0$ . Under certain assumptions on $f,g$ and $p\in \left(1,2\right)$ .