一类非线性SchrÖdinger方程多解的存在性

数学物理学报 ›› 2013, Vol. 33 ›› Issue (6): 1035-1044.

一类非线性SchrÖdinger方程多解的存在性

彭超权|马世超

中南民族大学 |数学与统计学学院武汉 430074

收稿日期:2012-02-20 修回日期:2013-03-08 出版日期:2013-12-25 发布日期:2013-12-25
基金资助:
中南民族大学中央高校基本科研业务费专项资金(CZY12013)和中南民族大学大学生创新创业训练计划(GCX12030)资助

The Existence of Nontrivial Solutions for a Class of Asymptotically Linear Equation

PENG Chao-Quan, MA Shi-Chao

College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074

Received:2012-02-20 Revised:2013-03-08 Online:2013-12-25 Published:2013-12-25
Supported by:
中南民族大学中央高校基本科研业务费专项资金(CZY12013)和中南民族大学大学生创新创业训练计划(GCX12030)资助

摘要/Abstract

摘要：

证明如下一类非线性SchrÖdinger方程
-Δu +V(x)u=f(x, u), x∈R^N多解的存在性, 其中N≥3, 位势V(x)关于x∈R^N连续, 并且对$\forall x∈R^N,有V(x)≥V₀>0. f(x, t) 为R^N×R上的连续函数并且在无穷远处关于t渐近线性或超线性.

关键词: 存在性, 多解, SchrÖdinger方程

Abstract:

In this paper, we show that the nonlinear SchrÖdinger equation
-Δu +V(x)u=f(x, u), x∈R^Npossesses multiple solutions in H¹(R^N), where N≥3 and the potential V(x) is a continuous function satisfying V(x)≥V₀>0 for all x∈R^N, f(x, t) is a continuous function in R^NR and asymptotically linear or superlinear at infinity for t.

Key words: Existence, Multiple solutions, SchrÖdinger equation

中图分类号:

35J60

彭超权, 马世超. 一类非线性SchrÖdinger方程多解的存在性[J]. 数学物理学报, 2013, 33(6): 1035-1044.

PENG Chao-Quan, MA Shi-Chao. The Existence of Nontrivial Solutions for a Class of Asymptotically Linear Equation[J]. Acta mathematica scientia,Series A, 2013, 33(6): 1035-1044.

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