一类非线性Schrodinger方程变号解的存在性

Existence of Sign Changing Solution fora Class of Nonlinear Schr dinger Equations

研究了一类非线性Schr dinger方程:-Δu+V x u=f x,u,x∈RN,其中f的原函数满足的超二次条件比(AR)条件更弱.利用下降流不变集方法,证明了该方程存在变号解.

In this paper,we consider a class of nonlinear Schr dinger equations-Δu+V x u=f x,u,x∈RN,where the super-quadratic conditions satisfied by the primitive of f are weaker than Ambrosetti-Rabinowitz type condition.By using the method of invariant sets of descending flow,we prove the existence of sign changing solution for this equation.