On the fourth-order Leray-Lions problem with indefinite weight and nonstandard growth conditions

TL;DR

This paper establishes the existence of multiple solutions for a complex fourth-order differential problem involving indefinite weights and nonstandard growth, expanding the understanding of such nonlinear PDEs.

Contribution

It introduces new existence results for fourth-order Leray-Lions problems with indefinite weights under nonstandard growth, using advanced variational methods.

Findings

Proves at least three weak solutions exist.

Utilizes the critical point theorem of Bonanno and Marano.

Extends solution theory to problems with indefinite weights and nonstandard growth.

Abstract

We prove the existence of at least three weak solutions for the fourth-order problem with indefinite weight involving the Leray-Lions operator with nonstandard growth conditions. The proof of our main result uses variational methods and the critical theorem of Bonanno and Marano (Appl. Anal. 89 (2010), 1-10).