we study the equation -Delta u + g(x, u) = mu, where g(., s) is finite outside sets of zero H-1-capacity, for all s is an element of R, and mu is a diffuse measure. As an application, we provide a positive answer to a question of Lucio Boccardo concerning existence of solutions of an elliptic system with absorption.
Orsina, L., & Ponce, A. (2008). Semilinear elliptic equations and systems with diffuse measures. Journal of Evolution Equations, 8(4), 781-812. https://doi.org/10.1007/s00028-008-0446-32 (Original work published 2008)