Sign changing solutions of the Brezis-Nirenberg problem in the Hyperbolic space

TL;DR

This paper investigates the existence, nonexistence, and asymptotic behavior of sign-changing solutions to a Brezis-Nirenberg type problem in hyperbolic space, providing insights into solution properties and compactness.

Contribution

It introduces new results on the existence and nonexistence of sign-changing solutions and establishes sharp asymptotic estimates in hyperbolic space.

Findings

Criteria for existence and nonexistence of solutions

Sharp asymptotic estimates for solutions

Analysis of compactness properties

Abstract

In this article we will study the existence and nonexistence of sign changing solutions for the Brezis-Nirenberg type problem in the Hyperbolic space. We will also establish sharp asymptotic estimates for the solutions and the compactness properties of solutions.