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.
Existence and Multiplicity Results for Semilinear Elliptic Equations with Measure Data and Jumping Nonlinearities
SACCON, CLAUDIO
2007-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
