Multiple solutions to quasi-linear elliptic Robin systems

TL;DR

This paper establishes the existence of multiple solutions for a non-variational p-Laplacian system with Robin boundary conditions using sub-super-solution and topological degree methods.

Contribution

It introduces new techniques to find multiple solutions to quasi-linear elliptic Robin systems, including the first nontrivial solution via topological degree.

Findings

Two constant-sign solutions found using sub-super-solution techniques

A third nontrivial solution identified through topological degree arguments

Results expand understanding of solution multiplicity in Robin boundary systems

Abstract

Two opposite constant-sign solutions to a non-variational p-Laplacian system with Robin boundary conditions are obtained via sub-super-solution techniques. A third nontrivial one comes out by means of topological degree arguments.