Sign-changing critical points from linking type theorems

作者：Martin Schechter, Wennan Zou · 发表于：Transactions of the American Mathematical Society · 年份：2006 · DOI：10.1090/s0002-9947-06-03852-9 · 被引用次数：31 · 研究领域：Stability and Controllability of Differential Equations、Nonlinear Differential Equations Analysis、Advanced Mathematical Physics Problems

In this paper, the relationships between sign-changing critical point theorems and the linking type theorems of M. Schechter and the saddle point theorems of P. Rabinowitz are established. The abstract results are applied to the study of the existence of sign-changing solutions for the nonlinear Schrödinger equation $-\Delta u +V(x)u = f(x, u), u \in H^1({\mathbf {R}}^N),$ where $f(x, u)$ is a Carathéodory function. Problems of jumping or oscillating nonlinearities and of double resonance are considered.