Small amplitude periodic solutions in time for one-dimensional nonlinear wave equations

DOI10.1007/S13324-016-0137-5zbMath1397.35153OpenAlexW2425592828MaRDI QIDQ1682224

Zhenjie Liu

Publication date: 29 November 2017

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13324-016-0137-5

zbMATH Keywords

Nash-Moser iterationsmall divisors

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to PDEs (35B10) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Implicit function theorems; global Newton methods on manifolds (58C15) Second-order semilinear hyperbolic equations (35L71)

Related Items (1)

Time periodic solutions of one-dimensional forced Kirchhoff equations with \(x\)-dependent coefficients under spatial periodic conditions

Cites Work

• Unnamed Item
• Unnamed Item
• An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation
• Branching of Cantor manifolds of elliptic tori and applications to PDEs
• An abstract Nash-Moser theorem with parameters and applications to PDEs
• Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions
• Cantor families of periodic solutions of wave equations with \(C^{k}\) nonlinearities
• Periodic solutions for the Schrödinger equation with nonlocal smoothing nonlinearities in higher dimension
• A Birkhoff-Lewis type theorem for the nonlinear wave equation
• Periodic solutions of nonlinear wave equations for asymptotically full measure sets of frequencies
• Multiplicity of periodic solutions of nonlinear wave equations.
• Periodic solutions for completely resonant nonlinear wave equations with Dirichlet boundary conditions
• Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method
• Nonlinear oscillations of Hamiltonian PDEs
• Periodic solutions for a class of nonlinear partial differential equations in higher dimension
• Cantor families of periodic solutions for wave equations via a variational principle
• Cantor families of periodic solutions for completely resonant nonlinear wave equations
• KAM theory for the Hamiltonian derivative wave equation
• Forced Vibrations of a Nonhomogeneous String
• Periodic solutions of forced Kirchhoff equations

This page was built for publication: Small amplitude periodic solutions in time for one-dimensional nonlinear wave equations