arXiv subjects
Publications and source records attributed to Mohammed Aldawood.
In this paper, we study a Bahri-Brezis type problem on a compact 3-dimensional asymptotically hyperbolic manifold. Using the celebrated Algebraic Topological argument of Bahri-Coron, we show the existence of at least one solution under the assumption that the corresponding degenerate boundary value problem has a positive first eigenvalue and a positive Green function.
In this paper, we study the Brezis-Nirenberg problem on bounded smooth domains of R3. Using the algebraic topological argument of Bahri-Coron[2] as implemented in [6] combined with the Brendle[4]- Schoen[8]'s bubble construction, we solve the problem for non-contractible domains.
In this paper, we study a Cherrier-Escobar problem for the extended problem corresponding to the elliptic Schroedinger-to-Neumann map on a compact 3-dimensional Riemannian manifold with boundary. Using the algebraic topological argument of Bahri-Coron, we show solvability under the assumption that the extended problem corresponding to the elliptic Schroedinger-to-Neumann map has a positive first eigenvalue, a positive Green function, and also verifies the strong maximum principle.