Existence results for quasilinear elliptic boundary value problems via topological methods

TL;DR

This paper establishes existence and localization results for solutions to quasilinear elliptic boundary value problems using topological methods, specifically the Leray-Schauder nonlinear alternative.

Contribution

It provides new existence results for $C^1$-solutions to elliptic boundary value problems via topological techniques, expanding the theoretical understanding.

Findings

Existence of $C^1$-solutions proven

Localization results for solutions obtained

Application of Leray-Schauder alternative in this context

Abstract

In this paper, existence and localization results of $C^1$-solutions to elliptic Dirichlet boundary value problems are established. The approach is based on the nonlinear alternative of Leray-Schauder.