On prescribed energy saddle-point solutions to indefinite problems

TL;DR

This paper introduces a minimax variational principle for finding saddle-point solutions with specific energy levels, using a linking theorem and nonlinear Rayleigh quotients, with applications to indefinite elliptic problems.

Contribution

It develops a new variational approach for saddle-point solutions at prescribed energy levels, extending existing methods to indefinite elliptic problems.

Findings

Existence of solutions with zero-energy levels.

Application of the linking theorem to energy level nonlinear Rayleigh quotients.

New variational framework for indefinite elliptic problems.

Abstract

A minimax variational principle for saddle-point solutions with prescribed energy levels is introduced. The approach is based on the development of the linking theorem to the energy level nonlinear generalized Rayleigh quotients. An application to indefinite elliptic Dirichlet problems is presented. Among the consequences, the existence of solutions with zero-energy levels is obtained.