Quasilinear elliptic equations with sub-natural growth terms in bounded domains

Abstract

We consider the existence of positive solutions to weighted quasilinear elliptic differential equations of the type −∆p,wu = σu q in Ω, u = 0 on ∂Ω in the sub-natural growth case 0 < q < p − 1, where Ω is a bounded domain in R n , ∆p,w is a weighted p-Laplacian, and σ is a Radon measure on Ω. We give criteria for the existence problem. For the proof, we investigate various properties of p-superharmonic functions, especially solvability of Dirichlet problems with non-finite measure data.