A jumping problem for quasilinear elliptic equations with right hand side measure

TL;DR

This paper investigates a quasilinear elliptic equation with a measure-based right hand side and a jumping-type lower order term, establishing the existence of one or two entropy solutions using degree theory techniques.

Contribution

It introduces a novel approach to handle jumping behavior in lower order terms for elliptic equations with measure data, proving existence results.

Findings

Existence of one entropy solution under certain conditions

Existence of two entropy solutions in some cases

Application of degree theory to jump-type problems

Abstract

We consider a quasilinear elliptic equation with right hand side measure, in which the lower order term has a behavior of jumping type. By means of techniques of degree theory, we prove the existence of one or two entropy solutions.