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 9(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 -> +/-infinity. 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
Ferrero, A., & Saccon, C. (2007). Existence and multiplicity results for semilinear elliptic equations with measure data and jumping nonlinearities. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 30(1), 37-65.