Existence Results For Semilinear Problems in the Two Dimensional Hyperbolic Space Involving Critical Growth

TL;DR

This paper investigates semilinear elliptic problems on two-dimensional hyperbolic space with critical growth, establishing existence of solutions and infinitely many sign-changing solutions using the Palais-Smale condition.

Contribution

It proves the existence of solutions and infinitely many sign-changing solutions for semilinear problems in hyperbolic space, extending previous results to critical growth scenarios.

Findings

Established the Palais-Smale condition for the problem

Proved existence of solutions using variational methods

Demonstrated existence of infinitely many sign-changing solutions

Abstract

We consider semilinear elliptic problems on two-dimensional hyperbolic space involving critical growth. We first establish the Palais-Smale(P-S) condition and using (P-S) condition we obtain existence of solutions. In addition, we also explore existence of infinitely many sign changing solutions as well.