Existence of positive solutions for a singular p-Laplacian differential equation

In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation $$ (\varphi _p (u'))' + \frac{\beta } {r}\varphi _p (u') - \gamma \frac{{|u'|^p }} {u} + g(r) = 0,0 < r < 1, $$ subject to the Dirichlet boundary conditions: u(0) = u(1) = 0, where ϕ p (s) = |s| p−2 s,p > 2, β > 0, γ > $$ \tfrac{{p - 1}} {p} $$ (β + 1), and g(r) ∈ C 1[0, 1] with g(r) > 0 for all r ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution.