Numerical analysis of semilinear elliptic equations with finite spectral interaction

Details Numerical analysis of semilinear elliptic equations with finite spectral interaction Numerical analysis of semilinear elliptic equations with finite spectral interaction

2011-07-28

arxiv.org/abs/1107.5783v1

Mathematics

Analysis of PDEs

20 pages, 15 figures (34 .eps files)

Scientific paper

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.

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