Existence of multiple positive solutions for singular p‐q‐Laplacian problems with critical nonlinearities

Abstract

In this article, we consider the following p‐q‐Laplacian system with singular and critical nonlinearity where Ω is a bounded domain in with smooth boundary ∂Ω. 1 < q < p < α + β = p∗, 0 < r < 1, α, β > 1, λ ∈ (0, Λ∗) is parameter and h1(x), h2(x) ∈ L∞, h1(x), h2(x) > 0. We show the existence and multiplicity of weak solution of equation above for suitable range of λ.