International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 10, Pages 1507-1523

Existence and uniqueness of solutions for a semilinear elliptic system

Robert Dalmasso

Equipe EDP, Laboratoire LMC-IMAG, Tour IRMA, BP 53, Grenoble Cedex 9 38041, France

Received 23 February 2005; Revised 4 May 2005

Copyright © 2005 Robert Dalmasso. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.