Sign-changing critical points from linking type theorems

Schechter, M.; Zou, W.

doi:10.1090/S0002-9947-06-03852-9

Sign-changing critical points from linking type theorems
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by M. Schechter and W. Zou PDF

Trans. Amer. Math. Soc. 358 (2006), 5293-5318 Request permission

Abstract:

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.

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