# Uniqueness for the Brezis-Nirenberg type problems on spheres and hemispheres

## TL;DR

This paper investigates Brezis-Nirenberg type nonlinear PDEs on spheres and hemispheres with Neumann boundary conditions, establishing conditions for solutions to be constant and extending results to systems.

## Contribution

It provides new conditions ensuring only constant solutions for these PDEs on spheres and hemispheres, including extensions to systems.

## Key findings

- Conditions for constant solutions on spheres and hemispheres
- Extension of results to nonlinear PDE systems
- Analysis of solutions under Neumann boundary conditions

## Abstract

In this work, we develop a study involving some nonlinear partial differential equations on spheres and hemispheres, with the zero Neumann boundary condition, which are so-called Brezis-Nirenberg type problems, and we give conditions on which such equations have only constant solutions. We also extend these results for some nonlinear partial differential systems.