Solutions for quasilinear fourth order elliptic equations on $\mathbb{R}^{N}$ with sign-changing potential

TL;DR

This paper establishes existence and multiplicity results for quasilinear fourth order elliptic equations on Euclidean space with potentials that change sign, extending recent findings in this area.

Contribution

It generalizes previous results by providing new existence and multiplicity theorems for these complex elliptic equations with sign-changing potentials.

Findings

Proved existence of solutions under broader conditions.

Established multiple solutions for the equations.

Extended previous results in the literature.

Abstract

We obtain existence and multiplicity results for quasilinear fourth order elliptic equations on $\mathbb{R}^{N}$ with sign-changing potential. Our results generalize some recent results on this problem.