Quasilinear elliptic problems with singular and homogeneous lower order terms

Abstract

We deal with singular quasilinear elliptic equations, namely −Δu=λu+μ(x)|∇u|quq−1+f(x)inΩ,u>0inΩ,u=0on∂Ω,where Ω is a bounded smooth domain of RN (N≥3), λ∈R, 1<q≤2, 0≤μ∈L∞(Ω) and 0≤f∈Lp(Ω) for some p>N2. We completely describe the set of values of the parameter λ for which the problem admits solution. Thus, we study existence, nonexistence and uniqueness of bounded weak solutions in both cases f⪈0 and f≡0.