Abstract

Let Ω⊂RN be a bounded domain with smooth boundary, a:Ω→[1,+∞) a bounded function, h:[0,+∞)→R continuous, and g:(0,+∞)→R a continuous function such that lims→0+g(s)=+∞. Fix p>1. This paper is concerned with the study of positive solutions of the singular elliptic equation −Δpu=ag(u)+λh(u) in Ω under the Dirichlet boundary condition u=0 on ∂Ω. In the first part of this paper it is established a sub- and super-solution theorem for this class of nonlinear problems. Then, there are established natural sufficient conditions that guarantee the existence of weak solutions to the above singular boundary value problem. The main point in the proof of the main result of the paper is the construction of a well-ordered pair of sub-supersolutions. The paper is well written and this reviewer considers that the results can be extended to the treatment of other classes of singular problems.