Numerical analysis of semilinear elliptic equations with finite spectral interaction

José Cal Neto; Carlos Tomei

Numerical analysis of semilinear elliptic equations with finite spectral interaction

Analysis of PDEs 2011-07-29 v1 Functional Analysis Numerical Analysis

Authors: José Cal Neto , Carlos Tomei

Abstract

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.

Keywords

semilinear elliptic equations finite spectral interaction non-resonant nonlinearities numerical algorithm Dirichlet boundary conditions Ambrosetti-Prodi theorem

Cite

@article{arxiv.1107.5783,
  title  = {Numerical analysis of semilinear elliptic equations with finite spectral interaction},
  author = {José Cal Neto and Carlos Tomei},
  journal= {arXiv preprint arXiv:1107.5783},
  year   = {2011}
}

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20 pages, 15 figures (34 .eps files)

Numerical analysis of semilinear elliptic equations with finite spectral interaction

Abstract

Keywords

Cite

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