带有零谱点的渐近线性薛定谔方程

Abstract

Abstract:

This paper is concerned with the following Schrödinger equation
-△u+V(x)u=f(x, u), for x∈R^N,
u(x)→0, as |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.

Key words: Schrödinger equation, Asymptotically linear, Spectrum point zero, Non-Nehari manifold method, Ground states solutions

CLC Number:

O175.29

Qin Dongdong, Li Yunyang, Tang Xianhua. Schrödinger Equation with Asymptotically Linear Nonlinearity and Spectrum Point Zero[J].Acta mathematica scientia,Series A, 2016, 36(6): 1103-1116.

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References

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Schrödinger Equation with Asymptotically Linear Nonlinearity and Spectrum Point Zero

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