带有次线性项薛定谔-麦克斯韦方程无穷多非平凡解的存在性

Existence of Infinitely Many Nontrivial Solutions for Schrdinger-Maxwell Equations with Sublinear Terms

该文主要讨论如下薛定谔-麦克斯韦方程无穷多解的存在性:{-△u+V(x)u+K(x)Фf(u)=g(x,u),在R^3中-△Ф=K(x)F(u)其中V(x)∈C(R^3,R),K∈L~∞(R^3,R),满足K≥0,并且F(u)=∫_0~uf(s)ds.在非线性项g满足次线性增长的条件下,利用变分法和喷泉定理得到该方程存在无穷多个非平凡解.

In this paper,we study the existence of infinitely many solutions for the Schrdinger-Maxwell equations,{-△u+V(x)u+K(x)Φf(u)=g(x,u),in R^3,-△Φ=K(x)F(u),in R^3 where V(x)∈C(R^3,R),K ∈L~∞(R^3) with K ≥0 and F(u)=∫_0~u f(s)ds.Considering the case wheregis sublinear,we prove the existence of infinitely many nontrival solutions by using the variational methods and fountain theorem.