Periodic solutions of forced Kirchhoff equations

DOI10.2422/2036-2145.2009.1.06zbMath1180.35040arXivmath/0701394OpenAlexW1644001879MaRDI QIDQ3647187

Pietro Baldi

Publication date: 30 November 2009

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701394

zbMATH Keywords

Dirichlet boundary conditionstime-periodic solutionsspace-periodic boundary conditionsNash-Moser iteration schemetime-periodic external forcing

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Integro-partial differential equations (45K05) Periodic solutions to PDEs (35B10) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Second-order semilinear hyperbolic equations (35L71)

Related Items (19)

KAM for autonomous quasi-linear perturbations of mKdV ⋮ Smooth quasi-periodic solutions for the perturbed mKdV equation ⋮ Time periodic solutions of one-dimensional forced Kirchhoff equations with x -dependent coefficients ⋮ A note on KAM theory for quasi-linear and fully nonlinear forced KdV ⋮ Time periodic solutions of one-dimensional forced Kirchhoff equation with Sturm-Liouville boundary conditions ⋮ Small amplitude periodic solutions in time for one-dimensional nonlinear wave equations ⋮ Reducibility in a certain matrix Lie algebra for smooth linear quasi-periodic system ⋮ Linearly stable KAM tori for one dimensional forced Kirchhoff equations with refined Töplitz-Lipschitz property ⋮ Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono type ⋮ Quasi-periodic solutions of forced Kirchhoff equation ⋮ Quasi-periodic solutions for the forced Kirchhoff equation on $ \newcommand{\m}{\mu} \newcommand{\T}{\mathbb T} \T^d$ ⋮ Time periodic solutions of one-dimensional forced Kirchhoff equations with \(x\)-dependent coefficients under spatial periodic conditions ⋮ A KAM theorem for higher dimensional wave equations under nonlocal perturbation ⋮ On the normal form of the Kirchhoff equation ⋮ Finite dimensional invariant KAM tori for tame vector fields ⋮ On the existence time for the Kirchhoff equation with periodic boundary conditions ⋮ Linearly stable KAM tori for higher dimensional Kirchhoff equations ⋮ Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations ⋮ Gravity capillary standing water waves

This page was built for publication: Periodic solutions of forced Kirchhoff equations