On quasi-linear equation problems involving critical and singular nonlinearities

Abstract

We consider the singular boundary value problemwhere Ω ⊂ R N (N 3) is a bounded domain such that 0 ∈ Ω, 0 < γ < 1, 0 a <is a given function. Based on different assumptions, using variational methods and Ekeland's principle, we admit that this problem possesses two positive solutions.