On positive viscosity solutions of fractional Lane-Emden systems

TL;DR

This paper investigates the existence, nonexistence, and uniqueness of positive viscosity solutions for fractional Lane-Emden systems on bounded domains, and identifies the critical hyperbola related to these systems.

Contribution

It provides new results on the conditions for existence and uniqueness of solutions and characterizes the critical hyperbola for fractional Lane-Emden systems.

Findings

Established criteria for existence and nonexistence of solutions.

Proved uniqueness of positive viscosity solutions under certain conditions.

Derived the critical hyperbola associated with the systems.

Abstract

We discuss on existence, nonexistence and uniqueness of positive viscosity solutions for Lane-Emden systems involving the fractional Laplacian on bounded domains. As a byproduct, we obtain the critical hyperbole associated to the these systems.