一类非线性Schrdinger-Maxwell方程组半经典解的存在性

Existence of semiclassical solutions for a class of Schrdinger-Maxwell equations

本文将研究如下非线性Schrdinger-Maxwell方程组问题{-ε2△u+V(x)u+K(x)φu=|u|p-2u,x∈R3,-△φ=4πK(x)u2,x∈R3.当势函数V(x)和电量函数K(x)满足一定假设条件时,作者利用变分法证明了ε充分小时,该方程组半经典解的存在性.

In this paper we discuss the existence of semiclassical solutions for the coupled Schrodinger-Maxwell equations{-ε^2△u＋V（x）u＋K（x）Фu=｜u｜^p-2u, x∈R^3, -△Ф=4πK（x）u^2, x∈R^3.Under suitable assumptions on V（x） and K（x）, we establish the existence results by critical point theory.