Max-Min characterization of the mountain pass energy level for a class of variational problems

TL;DR

This paper introduces a max-min characterization of the mountain pass energy level for certain variational problems, enabling the identification of solutions to PDEs with a mountain pass structure through classical minimization methods.

Contribution

It provides a novel max-min framework for the mountain pass energy level, linking variational principles to PDE solutions.

Findings

Established a max-min characterization for the mountain pass energy level.

Deduced the mountain pass structure of solutions to specific PDEs.

Connected classical minimization techniques to mountain pass solutions.

Abstract

We provide a max-min characterization of the mountain pass energy level for a family of variational problems. As a consequence we deduce the mountain pass structure of solutions to suitable PDEs, whose existence follows from classical minimization argument.