Existence of Singular Solutions for a Dirichlet Problem Containing a Dirac Mass

We give general existence results of solutions (u,v) to the Dirichlet problem {-?u=f(x,u,v)+c?0,-?v=g(x,u,v)+d? 0in D?(B),u=v=0on?B, where B is the unit ball centered at zero in ?N, N ? 3,?0 is the Dirac mass at 0 and c,d are nonnegative constants. No assumptions on the sign of the functions f and g are required. We also characterize the set of (c,d) such that problem (P) admits a solution in some particular cases of the nonlinearities f and g. © 2011 Elsevier Ltd. All rights reserved.