An Abstract Linking Theorem Applied to Indefinite Problems Via Spectral Properties

Abstract

An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite-dimensional Hilbert Spaces. The applications are given to Schrödinger equations. Here spectral properties inherited by the potential features are exploited in order to establish a linking structure, and hence hypotheses of monotonicity on the nonlinearities are discarded.

Keywords

• linking structure
• variational methods
• spectral theory
• schrödinger equation
• asymptotically linear
• 35j10
• 35j20
• 35j60
• 35p05