Infinite-dimensional non-linear ordinary differential equations and the KAM theory

DOI10.1070/RM1997V052N03ABEH001810zbMath0918.58025OpenAlexW2008082118MaRDI QIDQ4220853

Lev D. Pustyl'nikov

Publication date: 4 August 1999

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm1997v052n03abeh001810

zbMATH Keywords

KAM theorytravelling wave solutionsstability of solutionsinfinite-dimensional Hamiltonian systemsfamilies of periodic solutionswell-posed definitions

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Ordinary differential equations of infinite order (34A35) Qualitative theory for ordinary differential equations (34Cxx)

Related Items (6)

On the existence of periodic and bounded solutions for functional differential equations of pointwise type with a strongly nonlinear right-hand side ⋮ Existence of bounded soliton solutions in the problem of longitudinal oscillations of an elastic infinite rod in a field with a nonlinear potential of general form ⋮ Functional differential equations of pointwise type: bifurcation ⋮ Functional differential equations. Transl. from the Russian ⋮ Existence of Bounded Soliton Solutions for a Finite Difference Analogue of the Wave Equation with a Nonlinear Potential of General Form ⋮ Existence of bounded soliton solutions in the problem of longitudinal vibrations of an infinite elastic rod in a field with a strongly nonlinear potential

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