Variational approach for a class of cooperative systems

TL;DR

This paper uses variational methods to characterize coexistence states in cooperative systems and analyzes the blow-up behavior of solutions based on a key parameter.

Contribution

It introduces a variational approach to determine the existence of coexistence states in cooperative systems and studies their blow-up behavior.

Findings

Characterization of coexistence states using variational methods

Identification of parameter ranges leading to blow-up behavior

Insights into the solution structure of non-local equations

Abstract

The aim of this work is to ascertain the characterization of the existence of coexistence states for a class of cooperative systems supported by the study of an associated non--local equation through classical variational methods. Thanks to those results we are able to obtain the blow--up behaviour of the solutions in the whole domain for certain values of the main continuation parameter.