The Dirichlet problem for sublinear elliptic equations with source

Abstract

We present a necessary and sufficient condition on nonnegative Radon measures μ and ν for the existence of a positive continuous solution of the Dirichlet problem for the sublinear elliptic equation −Δu=μuq+ν with prescribed nonnegative continuous boundary data in a general domain. Moreover, two-sided pointwise estimates of Brezis–Kamin type for positive bounded solutions and the uniqueness of a positive continuous Lq-solution are investigated.