Existence of multiple solutions for a class of weighted p -Laplace equation

This article deals with the existence of weak solutions for the following weighted p-Laplace equation: {−div(μ(y)|∇w|p−2∇w)+h(y)|w|p−2w=λF(y)|w|α−2w+G(y)|w|β−2win Ω,w=0on ∂Ω, where Ω⊂RN(N≥ 3) is the bounded domain with smooth boundary ∂Ω, 0∈Ω, 10), λ>0 and μ is a Muckenhoupt weight. F(y),G(y) are continuous functions which change sign in Ω. Here, we establish the existence of at least two positive solutions by employing the Nehari manifold and the fibering map method.