Nonlinear oscillations of Hamiltonian PDEs

zbMath1146.35002MaRDI QIDQ2372410

Massimiliano Berti

Publication date: 27 July 2007

Published in: Progress in Nonlinear Differential Equations and Their Applications (Search for Journal in Brave)

zbMATH Keywords

mountain pass theorembifurcationcritical point theorynonlinear wave equationnonresonance conditionssmall divisorsNash-Moser theoryinfinite-dimensional Hamiltonian systemsvariational Lyapunov-Schmidt reductioncompletely resonant case

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Second-order nonlinear hyperbolic equations (35L70) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Resonance in context of PDEs (35B34) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

Related Items (20)

An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations ⋮ An abstract Nash-Moser theorem with parameters and applications to PDEs ⋮ Response solution to ill-posed Boussinesq equation with quasi-periodic forcing of Liouvillean frequency ⋮ Small amplitude periodic solutions in time for one-dimensional nonlinear wave equations ⋮ Nonsmooth Modal Analysis of Piecewise-Linear Impact Oscillators ⋮ Standing waves in a counter-rotating vortex filament pair ⋮ Families of Periodic Solutions for Some Hamiltonian PDEs ⋮ Existence of quasipattern solutions of the Swift-Hohenberg equation ⋮ On the continuation of degenerate periodic orbits via normal form: full dimensional resonant tori ⋮ Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces ⋮ An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations ⋮ Standing waves of fixed period for \(n+1\) vortex filaments ⋮ On the nonexistence of degenerate phase-shift multibreathers in Klein-Gordon models with interactions beyond nearest neighbors ⋮ On time periodic solutions to the conformal cubic wave equation on the Einstein cylinder ⋮ Resonant tori of arbitrary codimension for quasi-periodically forced systems ⋮ (Quasi)periodic solutions in (in)finite dimensional Hamiltonian systems with applications to celestial mechanics and wave equation ⋮ Torsional instability in suspension bridges: the Tacoma Narrows Bridge case ⋮ Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation ⋮ Long time behavior of a quasilinear hyperbolic system modelling elastic membranes ⋮ Quasi-periodic solutions of PDEs

This page was built for publication: Nonlinear oscillations of Hamiltonian PDEs