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

We consider the existence of positive solutions to weighted quasilinear elliptic differential equations of the type - Δ p , w u = σ u 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 , Δ p , w is a weighted p-Laplacian, and σ is a nonnegative (locally finite) Radon measure on Ω . We give criteria for the existence problem. For the proof, we investigate various properties of p-superharmonic functions, especially the solvability of Dirichlet problems with infinite measure data. [ABSTRACT FROM AUTHOR]