International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 10, Pages 1507-1523
doi:10.1155/IJMMS.2005.1507

Existence and uniqueness of solutions for a semilinear elliptic system

Abstract

We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equation Δ2u=|u|p in a ball with p>0.