Existence of solutions for some systems of superdiffusive integro-differential equations in population dynamics depending on the natality and mortality rates

TL;DR

This paper establishes the existence of stationary solutions for certain superdiffusive reaction-diffusion systems in population dynamics, considering the effects of natality and mortality rates using fixed point theorems.

Contribution

It introduces a novel approach to proving solutions for superdiffusive systems with complex differential operators influenced by population rates.

Findings

Existence of solutions proven for superdiffusive systems

Method based on fixed point theorem with Fredholm property considerations

Results depend on competition between natality and mortality rates

Abstract

We prove the existence of stationary solutions for some systems of reaction-diffusion type equations with superdiffusion in the corresponding H^2 spaces. Our method is based on the fixed point theorem when the elliptic problems contain first order differential operators with and without the Fredholm property, which may depend on the outcome of the competition between the natality and the mortality rates contained in the equations of our systems.