The spectrum of the periodic \(p\)-Laplacian

DOI10.1016/j.jde.2006.11.019zbMath1218.34100OpenAlexW2056876155MaRDI QIDQ876875

Bryan P. Rynne, Paul A. Binding

Publication date: 19 April 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.11.019

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05)

Related Items (17)

Simple bifurcation and global curves of solutions of \(p\)-Laplacian problems with radial symmetry ⋮ Landesman-Lazer conditions for resonant \(p\)-Laplacian problems with jumping nonlinearities ⋮ On the structure of periodic eigenvalues of the vectorial p-Laplacian ⋮ Unnamed Item ⋮ Nonlinear resonant periodic problems with concave terms ⋮ Exact multiplicity and stability of solutions of a 1-dimensional, \(p\)-Laplacian problem with positive convex nonlinearity ⋮ Exact multiplicity of positive solutions for a \(p\)-Laplacian equation with positive convex nonlinearity ⋮ Minimization of eigenvalues of one-dimensional \(p\)-Laplacian with integrable potentials ⋮ Oscillation and interlacing for various spectra of the \(p\)-Laplacian ⋮ Continuity in weak topology and extremal problems of eigenvalues of the $p$-Laplacian ⋮ Solutions and multiple solutions for superlinear perturbations of the periodic scalar p-Laplacian ⋮ Variational and non-variational eigenvalues of the \(p\)-Laplacian ⋮ Spectrum of one-dimensional \(p\)-Laplacian with an indefinite integrable weight ⋮ Some remarks on a nonhomogeneous eigenvalue problem related to generalized trigonometric functions ⋮ Linearized stability implies dynamic stability for equilibria of 1-dimensional, p-Laplacian boundary value problems ⋮ Positive solutions for nonlinear periodic problems ⋮ Nonresonance conditions for generalised \(\phi\)-Laplacian problems with jumping nonlinearities

Cites Work

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• Half-eigenvalues of periodic Sturm--Liouville problems
• Spectral analysis of nonlinear operators
• Sturm-Liouville type problems for the \(p\)-Laplacian under asymptotic non-resonance conditions
• The existence of solutions to a class of semilinear differential equations
• A local bifurcation theorem for degenerate elliptic equations with radial symmetry
• On the closed solution to some nonhomogeneous eigenvalue problem with \(p\)-Laplacian
• A Landesman-Lazer type theorem for periodic solutions of the resonant asymmetric \(p\)-Laplacian equation
• THE ROTATION NUMBER APPROACH TO EIGENVALUES OF THE ONE-DIMENSIONAL p-LAPLACIAN WITH PERIODIC POTENTIALS
• Existence and multiplicity of solutions with prescribed period for a second order quasilinear O.D.E.
• Sturm--Liouville theory for the p-Laplacian
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations

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