Multiple positive solutions for singular elliptic equations with weighted Hardy terms and critical Sobolev–Hardy exponents

Abstract

Variational methods are used to prove the multiplicity of positive solutions for the following singular elliptic equation:where 0 ∈ Ω ⊂ ℝN, N ≥ 3, is a bounded domain with smooth boundary ∂ Ω, λ > 0 , $1\le q<2$, $0\le\mu<\bar{\mu}=(N-2)^2/4$, 0 ≤ s < 2, 2*(s)=2(N−s)/(N−2) and f and g are continuous functions on $\bar{\varOmega}$, that change sign on Ω.