Existence and multiplicity results for semilinear ellipctic equations with measure data and jumping nonlinearities
Słowa kluczowe
Semilinear equations, Radon measures, critical point theoryAbstrakt
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 $u\rightarrow\pm \infty$. 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.Pobrania
Opublikowane
2007-09-01
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1.
FERRERO, Alberto & SACCON, Claudio. Existence and multiplicity results for semilinear ellipctic equations with measure data and jumping nonlinearities. Topological Methods in Nonlinear Analysis [online]. 1 wrzesień 2007, T. 30, nr 1, s. 37–65. [udostępniono 22.7.2024].
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