带有零谱点的渐近线性薛定谔方程

Schrdinger Equation with Asymptotically Linear Nonlinearity and Spectrum Point Zero

该文考虑了如下薛定谔方程{-△u+V(x)u=f(x,u),对x∈R^N,u(x)→0,当|x|→∞,其中V与f关于x是周期的,0是谱σ(-△+V)的一个边界点.受最近的文献[35]的启发,进一步考虑了f(x,u)在|u|→∞时是渐近线性的情况,并利用非Nehari流形方法得到了该方程的基态解.与广义Nehari流形方法相比,该方法更加简便、直接.

This paper is concerned with the following Schrodinger equation {-△u＋V（x）u=f（x,u）,对x∈R^N,u（x）→0,当｜x｜→∞ where V and f are both periodic in x and 0 is a boundary point of the spectrum σ（-△＋V）. Inspired by recent work of Tang[35], we consider further the case that f（x, u） is asymptotically linear as ｜u｜→∞, and obtain the existence of ground state solutions using the non-Nehari manifold method which is more direct and simpler than the generalized manifold method.