We study existence and multiplicity results for semilinear elliptic equations of the type −∆u = g(x, u) − te1 + µ with homogeneous Dirichlet boundary conditions. Here g(x, u) is a jumping nonlinearity, µ is a Radon measure, t is a positive constant and e1 > 0 is the first eigenfunction of −∆. Existence results strictly depend on the asymptotic behavior of g(x, u) as u → ±∞. Depending on this ... [Show full abstract] asymptotic behavior, we prove existence of two and three solutions for t > 0 large enough. In order to find solutions of the equation, we introduce a suitable action functional It by mean of an appropriate iterative scheme. Then we apply to It standard results from the critical point theory and we prove existence of critical points for this functional.