Existence of a continuum of solutions for a quasilinear elliptic singular problem

In this paper we study the existence of positive solution u∈H01(Ω) for some quasilinear elliptic equations, having lower order terms with quadratic growth in the gradient and singularities, whose model is−Δu+μ(x)|∇u|2uγ+uβ=λup+f0(x),x∈Ω,0<γ≤β,00λ>0 if 1<γ<21<γ<2 for any β   and p<1p<1. Even more for μ∈L∞(Ω)μ∈L∞(Ω) we prove this result if β≤1β≤1 and p<2−βp<2−β.