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Computing eigenvalues and Fučik-spectrum of the radially symmetric \(p\)-Laplacian. (English) Zbl 1020.65083

From the authors’ abstract: Eigenvalue problems for the radially symmetric \(p\)-Laplacian are discussed. We present algorithms which compute a given number of eigenvalues and Fučík-curves together with the corresponding eigenfunctions. The second-order \(p\)-Laplacian equation is transformed into a first-order system by a generalized Prüfer-transformation. To the first-order system we apply shooting algorithms, Newton’s method and in case of the Fučík-curves a predictor-corrector method. Singular as well as regular problems are treated, and a detailed error analysis for the approximation of singular problems by regular ones are given. Numerical results are presented.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems

Software:

nag; SLEDGE; SLEIGN2; d02kef
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Full Text: DOI

References:

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