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.

Existence and multiplicity results for semilinear elliptic equations with measure data and jumping nonlinearities

Ferrero, A;
2007

Abstract

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
Articolo in rivista - Articolo scientifico
semilinear equations; Radon measures; critical point theory
Equazioni, differenziali
English
2007
30
1
37
65
none
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/7700
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