On weak solutions for fourth-order problems involving the Leray-Lions type operators

TL;DR

This paper studies the existence and multiplicity of weak solutions for complex fourth-order differential problems involving Leray-Lions operators in variable exponent spaces, enhancing previous results with advanced variational methods.

Contribution

It introduces new existence and multiplicity results for these problems using variational techniques, improving upon earlier work by Bonanno and Chinni (2011).

Findings

Established new conditions for solution existence.

Proved multiple solutions under certain assumptions.

Extended previous results to variable exponent spaces.

Abstract

We investigate existence and multiplicity of weak solutions for fourth-order problems involving the Leray-Lions type operators in variable exponent spaces and improve a result of Bonanno and Chinn\`{i} (2011). We use variational methods and apply a multiplicity theorem of Bonanno and Marano (2010).