Unilateral global bifurcation for a class of quasilinear elliptic systems and applications

TL;DR

This paper proves a new unilateral bifurcation theorem for strongly coupled quasilinear elliptic systems, extending previous results, and applies it to population dynamics models to identify coexistence states.

Contribution

It extends a bifurcation theorem to a broader class of coupled quasilinear elliptic systems using advanced operator theory and eigenvalue analysis.

Findings

Established a unilateral bifurcation result for quasilinear elliptic systems

Applied the theorem to population dynamics models

Identified regions where coexistence states exist

Abstract

In this paper we establish a unilateral bifurcation result for a class of quasilinear elliptic system strongly coupled, extending a bifurcation theorem due to J. L\'opez-G\'omez. To this aim, we use several results, such that Fredholm operator of index $0$ theory, eigenvalues of elliptic operators and the Krein-Rutman theorem. Lastly, we apply this result to some particular systems arising from population dynamics and determine a region of existence of coexistence states.