中文摘要：

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.

英文摘要：

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.