带有临界指标的周期Schrödinger方程的基态解

数学物理学报 ›› 2015, Vol. 35 ›› Issue (4): 651-655.

带有临界指标的周期Schrödinger方程的基态解

许娜, 马世旺

南开大学数学科学学院, 天津 300071

收稿日期:2014-03-28 修回日期:2014-10-21 出版日期:2015-08-25 发布日期:2015-08-25
作者简介:许娜, weila319@163.com;马世旺, shiwangm@163.net
基金资助:
国家自然科学基金(11171163)资助

Ground State Solutions for A Periodic Schrödinger Equation with Critical Sobolev Exponent

Xu Na, Ma Shiwang

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071

Received:2014-03-28 Revised:2014-10-21 Online:2015-08-25 Published:2015-08-25

摘要/Abstract

摘要：

该文证明周期 Schrödinger方程
-Δ u +V(x)u=K(x)|u|^{2^*-2} u+g(x,u), u∈ H¹(R^N)
基态解的存在性, 其中 N≥ 4, 2^*=(2N)/(N-2) 为临界 Sobolev 指标. 该文补充了以上方程关于基态解存在性的以往结果.

关键词: 基态解, 临界指标, 环绕

Abstract:

In this note, we obtain the existence of ground state solutions for the following periodic Schrödinger equation
-Δ u +V(x)u=K(x)|u|^{2^*-2} u+g(x,u), u∈ H¹(R^N),
where N≥ 4 and 2^*=(2N)/(N-2) is the critical Sobolev exponent. Our result is a complement to some recent works concerning the existence of ground state solutions of the above equation.

Key words: Ground state solution, Critical Sobolev exponent, Linking

中图分类号:

O175.25

许娜, 马世旺. 带有临界指标的周期Schrödinger方程的基态解[J]. 数学物理学报, 2015, 35(4): 651-655.

Xu Na, Ma Shiwang. Ground State Solutions for A Periodic Schrödinger Equation with Critical Sobolev Exponent[J]. Acta mathematica scientia,Series A, 2015, 35(4): 651-655.

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