Radially symmetric solutions to the H\`enon-Lane-Emden system on the critical hyperbola

TL;DR

This paper investigates the existence and properties of radially symmetric solutions to the Hènon-Lane-Emden system with weights, focusing on the critical hyperbola, using variational methods and exploring nonexistence results.

Contribution

It introduces a variational approach to find radially symmetric solutions on the critical hyperbola and discusses their qualitative properties and nonexistence conditions.

Findings

Existence of nontrivial radially symmetric solutions on the critical hyperbola.

Qualitative properties of solutions are characterized.

Nonexistence results are established under certain conditions.

Abstract

We use variational methods to study the existence of nontrivial and radially symmetric solutions to the H\`enon-Lane-Emden system with weights, when the exponents involved lie on the "critical hyperbola". We also discuss qualitative properties of solutions and nonexistence results.