We study existence and multiplicity results for semilinear elliptic equations of the type −∆u = g(x, u) − te_1 + 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 e_1 > 0 is the first eigenfunction of −∆. Existence results strictly depend on the asymptotic behavior of g(x, u) as u → ±∞. 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 means 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.
|Autori:||FERRERO ALBERTO; SACCON C|
|Titolo:||Existence and Multiplicity Results for Semilinear Elliptic Equations with Measure Data and Jumping Nonlinearities|
|Anno del prodotto:||2007|
|Appare nelle tipologie:||1.1 Articolo in rivista|