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arXiv:1107.5783 [math.AP]AbstractReferencesReviewsResources

Numerical analysis of semilinear elliptic equations with finite spectral interaction

José Cal Neto, Carlos Tomei

Published 2011-07-28Version 1

We present an algorithm to solve $- \lap u - f(x,u) = g$ with Dirichlet boundary conditions in a bounded domain $\Omega$. The nonlinearities are non-resonant and have finite spectral interaction: no eigenvalue of $-\lap_D$ is an endpoint of $\bar{\partial_2f(\Omega,\RR)}$, which in turn only contains a finite number of eigenvalues. The algorithm is based in ideas used by Berger and Podolak to provide a geometric proof of the Ambrosetti-Prodi theorem and advances work by Smiley and Chun for the same problem.

Comments: 20 pages, 15 figures (34 .eps files)
Categories: math.AP, math.FA, math.NA
Subjects: 35B32, 35J91, 65N30
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