一类非线性Choquard方程基态解的存在性

Existence of Positive Ground State Solutions for the Choquard Equation

该文研究如下一类非线性Choquard方程-△u+V(x)u=(I_(α)a*F(u))f(u),x∈R^(N),其中N≥3,α∈(0,N),I_(α)是Riesz势,位势函数V:R^(N)→R为连续函数,F∈C^(1)(R,R),且F’(s)=f(s).在函数V和f满足合适的条件下(但f不必满足(AR)条件),利用变分方法,该文证明了上述方程存在一个正的基态解.

In this paper we study the following nonlinear Choquard equation-△u+V(x)u=(I_(α)a*F(u))f(u),x∈R^(N),where N≥3,α∈(0,N),I_(α) is the Riesz potential,V(x):R^(N)→R is a given potential function,and F∈C^(1)(R,R)with F’(s)=f(s).Under assumptions on V and f,we do not require the(AR)condition of f,the existence of ground state solutions are obtained via variational methods.