R^N中一类Schrdinger方程非平凡解的存在性

The Existence of Nontrivial Solution for a Class of Schrdinger Equation in R^N

研究了一类非线性Schrdinger方程-Δu+V(x)u=f(u),x∈RN,在H1(RN)中非平凡解的存在性,其中N≥3,位势V(x)是RN上的连续函数,并且存在V0>0,使得对x∈RN,都有V(x)≥V0>0.

In this paper,we study that the nonlinear Schrodinger equation --△u＋V（x）u=f（u）,x∈R^N,possesses at least one nontrivial solution in H^1 （R^N） ,where N≥3 and the potential V（x） is a continuous function, satisfying V（x）≥V0〉O for all x∈R^N.