On the existence and multiplicity results for a class of elliptic problems with singular weights and failing zeroes

Abstract

In this paper, we consider the existence of positive solutions to singular elliptic problems of the form

-div(|x|^-ap|∇ u|^p-2∇ u) = λ|x|^-(a+1)p+b f(u), x∈ Ω,

u=0                                                         x∈ ∂Ω,   

where Ω is a bounded smooth domain of R^N with 0∈ Ω, 1 < p < N, 0 ≤ a < (N-p)/p and b, λ are positive parameters. Here f : [0, ∞ ) R is continuous function. We discuss the existence of a positive solution when f satisfies certain additional conditions. We use the method of sub-super solutions to establish our results.