Non-variational weakly coupled elliptic systems

TL;DR

This paper proves the existence of nonnegative solutions for a class of non-variational weakly coupled elliptic systems using topological and degree-theoretical methods.

Contribution

It introduces a novel approach to establish solutions in non-variational elliptic systems by leveraging a Nehari-type manifold and degree theory.

Findings

Existence of nonnegative fully nontrivial solutions

Solutions form a topological manifold of Nehari-type

Application of degree theory to prove existence

Abstract

We establish the existence of a nonnegative fully nontrivial solution to a non-variational weakly coupled competitive elliptic system. We show that this kind of solutions belong to a topological manifold of Nehari-type, and apply a degree-theoretical argument on this manifold to derive existence.