We study the existence of positive weak solutions to a fourth-order semilinear elliptic equation with Navier boundary conditions and a positive, increasing and convex source term. We also prove the uniqueness of extremal solutions. In particular, we generalize results of Mironescu and Rădulescu for the bi-Laplacian operator.
The existence of singular limit solutions are investigated by establishing a new Liouville type theorem for nonlinear elliptic system by using the Pohozaev type identity and the nonlinear domain decomposition method.
We study existence of solutions with singular limits for a 2-dimensional semilinear elliptic problem with exponential dominated nonlinearity and a singular source term given by Dirac masses, imposing Dirichlet boundary condition. This paper extends previous results obtained in [3, 8]. We mainly use the method of domain decomposition.
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