NONTRIVIAL SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS WITH MEASURE DATA

The main subject of this thesis is the study, by a variational approach, of semilinear elliptic problems with measure data. Starting with a semilinear problem with unique solution, we introduce a parametrized perturbation and study the bifurcation phenomena giving rise to further solutions. The main feature is that we are able to use a direct variational approach, even when the semilinearity has no growth assumptions. In this setting, we prove bifurcation results in the line of classical results of Boehme-Marino and Rabinowitz and also global existence results.