Existence, nonexistence and multiplicity results for semilinear elliptic problems with measure data and absorption-reaction term

Abstract

In the case where g(u) appears as an absorption term, then under some additional hypotheses on g we prove that the main problem has a solution for all lambda >0 and for all positive mu is an element of L-1(Omega). In the case where g appears as a reaction term, then we prove that the main problem has at least two positive solutions under suitable hypotheses on mu. The asymptotic linear case is also studied.