Computing eigenvalues and Fučik-spectrum of the radially symmetric \(p\)-Laplacian

DOI10.1016/S0377-0427(02)00581-2zbMath1020.65083MaRDI QIDQ1860441

B. Malcolm Brown, Wolfgang Reichel

Publication date: 23 February 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

algorithmsnumerical resultsNewton's methoderror analysispredictor-corrector methodeigenfunctionsnonlinear eigenvalue problem\(p\)-Laplacianshooting algorithmsFučík-spectrumPrüfer-transformation

Mathematics Subject Classification ID

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

Related Items

Asymptotic behavior of the curves in the Fučík spectrum, Eigenvalues of the radial \(p\)-Laplacian with a potential on \((0,\infty)\), Bounds for the positive eigenvalues of the \(p\)-Laplacian with decaying potential, Precise homogenization rates for the Fučík spectrum, Inverse power method for the principal eigenvalue of the Robin \(p\)-Laplacian, The second eigenfunction of the \(p\)-Laplacian on the disk is not radial, Analytical and numerical results for the Fučík spectrum of the Laplacian., On the existence of sign-changing radial solutions to nonlinear \(p\)-Laplacian equations in \(\mathbb R^n\), Computing the first eigenpair of the \(p\)-Laplacian in annuli, Titchmarsh's asymptotic formula for periodic eigenvalues and an extension to the \(p\)-Laplacian, On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae, Computing the best constant in the Sobolev inequality for a ball, Unnamed Item

Uses Software

• SLEDGE
• SLEIGN2
• nag
• d02kef

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global bifurcation from the eigenvalues of the \(p\)-Laplacian
• Automatic solution of Sturm-Liouville problems using the Pruess method
• Some remarkable sine and cosine functions
• Sturm-Liouville type problems for the \(p\)-Laplacian under asymptotic non-resonance conditions
• Radial Fučik spectrum of the Laplace operator
• On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• Mathematical software for Sturm-Liouville problems
• Algorithm 810: The SLEIGN2 Sturm-Liouville Code
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations