Numerical analysis of semilinear elliptic equations with finite spectral interaction

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Cal Neto, Jose Teixeira²  Tomei, Carlos¹ 

[1] Pontificia Univ Catolica Rio de Janeiro, Dept Matemat, BR-22453900 Rio de Janeiro, Brazil

[2] Univ Fed Estado Rio de Janeiro, Dept Matemat & Estat, BR-22290240 Rio de Janeiro, Brazil

关键词: Semilinear elliptic equations;    Finite element methods;    Lyapunov-Schmidt decomposition;   

DOI  :  10.1016/j.jmaa.2012.04.073

来源: Elsevier

【 摘 要 】

We present an algorithm for solving -Delta 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 -Delta(D) is an endpoint of <(partial derivative(2)f(Omega, R))over bar>, which in turn only contains a finite number of eigenvalues. The algorithm is based on ideas used by Berger and Podolak to provide a geometric proof of the Ambrosetti-Prodi theorem and advances work by Smiley and Chun on the same problem. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free