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

preprint2021arXivOpen access

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.

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