A Fredholm alternative for quasilinear elliptic equations with right hand side measure

TL;DR

This paper establishes an existence result for a class of quasilinear elliptic equations with measure data, extending the Fredholm alternative by developing a specialized degree theory without the usual coercivity assumption.

Contribution

It introduces a novel degree theory variant to prove existence results for quasilinear elliptic equations with measure right-hand sides lacking coercivity.

Findings

Existence of solutions under non-coercive conditions

Development of a new degree theory variant

Extension of Fredholm alternative to measure data

Abstract

We consider a quasilinear elliptic equation, with right hand side measure, which does not satisfy the usual coercivity assumption. We prove an existence result in the line of the Fredholm alternative. For this purpose we develop a variant of degree theory suited to this setting.