Existence of nonnegative solutions for singular elliptic problems
Abstract
We prove the existence of nonnegative nontrivial weak solutions to the problem −∆u = au−αχ{u>0} − bup in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in Rn. A sufficient condition for the existence of a continuous and strictly positive weak solution is also given, and the uniqueness of such a solution is proved. We also prove a maximality property for solutions that are positive a.e. in Ω.