Existence and multiplicity of positive solutions for singular p&q-Laplacian problems via sub-supersolution method

Abstract

In this work we show the existence and multiplicity of positive solutions for a singular elliptic problem which the operator is non-linear and non-homogenous. We use the sub-supersolution method to study the following class of p&q-singular problems. -div (a(|∇u|^p)|∇u|p-2∇u) = h(x)u−γ + ƒ(x, u) in Ω, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝN with N ≥ 3, 2 ≤ p < N and γ > 0. The hypotheses on the functions α, h, and ƒ allow us to extend this result to a large class of problems.