Mountain pass solutions for quasi-linear equations via a monotonicity trick

TL;DR

This paper establishes the existence of mountain pass solutions for quasi-linear equations using a novel monotonicity trick, extending results even to the p-Laplacian operator without standard boundedness assumptions.

Contribution

It introduces a new approach employing a recent monotonicity trick to prove solutions for quasi-linear equations without typical boundedness conditions.

Findings

Existence of mountain pass solutions for quasi-linear equations.

Extension of results to the p-Laplacian operator.

Application of a recent monotonicity trick to nonlinear PDEs.

Abstract

We obtain the existence of mountain pass solutions for quasi-linear equations without the typical assumptions which guarantee the boundedness of an arbitrary Palais-Smale sequence. This is done through a recent version of the monotonicity trick proved by the second author. The main results are new also for the p-Laplacian operator.