Supercritical Henon type equation with a forcing term

TL;DR

This paper investigates the solution structure of a supercritical Henon type elliptic equation with a forcing term, providing a complete classification of when solutions exist or do not exist under certain conditions.

Contribution

It offers a comprehensive classification of solution existence for a supercritical Henon type equation with forcing, extending understanding of such elliptic problems.

Findings

Complete classification of existence and nonexistence of solutions

Conditions on the forcing term that determine solution behavior

Insights into the structure of solutions for supercritical equations

Abstract

This paper is concerned with the structure of solutions to the elliptic problem for an Henon type equation with a forcing term. Under suitable assumptions on the forcing term, we give a complete classification of the existence/nonexistence of solutions to the problem.