Increasing variational solutions for a nonlinear $p$-laplace equation without growth conditions

TL;DR

This paper introduces a new variational method to establish the existence of radially monotone solutions for nonlinear p-Laplace equations without relying on traditional growth conditions, expanding the scope of solvable problems.

Contribution

It presents a novel variational approach that removes the need for subcriticality conditions in solving nonlinear p-Laplace equations.

Findings

Existence of radially monotone solutions proven

No subcriticality condition required

Method applicable to a broad class of nonlinear problems

Abstract

By means of a recent variational technique, we prove the existence of radially monotone solutions to a class of nonlinear problems involving the $p$-Laplace operator. No subcriticality condition (in the sense of Sobolev spaces) is required.