Positive solutions for Dirichlet problems of singular quasilinear elliptic equations via variational methods

Abstract

This paper studies the existence and multiplicity of positive solutions of the following problem: (*) where Ω⊂RN(N≥3) is a smooth bounded domain, , 1 < p < N, and 0 < α < 1, p - 1 < β < p* - 1 (p* = Np/(N - p)) and 0 < γ < N + ((β + 1)(p - N)/p) are three constants. Also δ(x) = dist(x, ∂Ω), a ∈ Lp and λ < 0 is a real parameter. By using the direct method of the calculus of variations, Ekeland's Variational Principle and an idea of G. Tarantello, it is proved that problem (*) has at least two positive weak solutions if λ is small enough.