Min-max level estimate for a singular quasilinear polyharmonic equation in $\mathbb{R}^{2m}$

TL;DR

This paper establishes an Adams type inequality within a specific framework, estimates the min-max level of a nonlinear functional under certain conditions, and applies these results to prove multiplicity of solutions for a singular quasilinear elliptic equation.

Contribution

It introduces a new Adams type inequality in the context of singular quasilinear polyharmonic equations and estimates the min-max level for associated functionals.

Findings

Established an Adams type inequality for the framework of Ruf and Sani.

Estimated the min-max level of the nonlinear functional under two assumptions.

Proved a multiplicity result for solutions of the singular quasilinear elliptic equation.

Abstract

Using the framework first presented by Ruf and Sani, we give a proof of an Adams type inequality which can be applied to a nonlinear functional. Under two kinds of assumptions on the nonlinearity, we estimate the min-max level of the functional. As an application, a multiplicity result for the related singular quasilinear elliptic equation is proved.