An abstract linking theorem applied to indefinite problems via spectral properties

TL;DR

This paper introduces an abstract linking theorem that bypasses the Cerami condition, enabling the proof of critical points in indefinite problems using spectral properties, with applications to Hamiltonian systems and Schrödinger equations.

Contribution

It presents a new linking theorem applicable without the Cerami condition, utilizing spectral properties to handle indefinite problems in infinite-dimensional Hilbert spaces.

Findings

Established a linking theorem without Cerami condition

Proved existence of critical points for indefinite problems

Applied results to Hamiltonian systems and Schrödinger equations

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 main applications are given to Hamiltonian systems and Schrodinger equations. Here spectral properties of the operators are exploited and hypotheses of monotonicity on the nonlinearities are discarded.