Existence of a positive solution for nonlinear Schrödinger equations with general nonlinearity

Advances in Nonlinear Analysis

article

Yohei Sato¹  Masataka Shibata³ 

[1] Department of Mathematics, Saitama University;Osaka City University Advanced Mathematical Institute;Department of Mathematics, Tokyo Institute of Technology

关键词: Variational method;    nonlinear Schrödinger equation;    positive solution;   

DOI  :  10.1515/anona-2014-0003

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We study the following nonlinear Schrödinger equations: -Δu+V(x)u=f(u)inℝN.$ - \Delta u + V(x) u = f(u) \quad \text{in } {\mathbb {R}^N}. $ The purpose of this paper is to establish the existence of a positive solution under general conditions which are weaker than the Ambrosetti–Rabinowitz condition.

【 授权许可】

CC BY