A singularity as a break point for the multiplicity of solutions to quasilinear elliptic problems

Abstract

In this paper we deal with the elliptic problem-Δu=λu+μ(x)|∇u|quα+f(x) in ω,u>0 in ω,u=0 on δω, where ω ⊂ RN is a bounded smooth domain, 0 ≤ μ &insin; L∞(ω), 0 ≤ f Ε Lp0(ω) for some p0 > N2 1 < q < 2, α &insin; [0 1] and λ &insin; R. We establish existence and multiplicity results for λ > 0 and α 0 and q-1