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The first eigenvalue and eigenfunction of a nonlinear elliptic system. (English) Zbl 1429.35165

The principal eigenvalue and eigenfunctions of an elliptic system involving the \(p\)-Laplace operator are analysed analytically and numerically. Indeed, besides an alternative proof for the simplicity of the first eigenvalue of the system, a numerical algorithm to compute approximate principal eigenvalues and corresponding eigenfunctions is presented. The algorithm is applied to several concrete cases.

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

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