Existence and multiplicity results for semilinear elliptic equations with measures and jumping nonlinearities

We study existence and multiplicity results for semilinear elliptic equations of the type -\Delta u = g(x, u) - te_1 + \mu with homogeneous Dirichlet boundary conditions. Here g(x, u) is a jumping nonlinearity, \mu is a Radon measure, t is a positive constant and e_1 > 0 is the first eigenfunction of -\Delta. Existence results strictly depend on the asymptotic behavior of g(x, u) as u -> \pm \infty. Depending on this 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 I_t by mean of an appropriate iterative scheme. Then we apply to I_t standard results from the critical point theory and we prove existence of critical points for this functional.