Existence and multiplicity results for semilinear ellipctic equations with measure data and jumping nonlinearities
Keywords
Semilinear equations, Radon measures, critical point theoryAbstract
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.Downloads
Published
2007-09-01
How to Cite
1.
FERRERO, Alberto and SACCON, Claudio. Existence and multiplicity results for semilinear ellipctic equations with measure data and jumping nonlinearities. Topological Methods in Nonlinear Analysis. Online. 1 September 2007. Vol. 30, no. 1, pp. 37 - 65. [Accessed 28 March 2024].
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