Quasi-periodic solutions for a completely resonant beam equation with a nonlinear term depending on the time and space variables

Wang, Yi

doi:10.1016/j.na.2019.111585

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“…KAM theory [21,33] and Nash-Moser iteration technique [2,15] are derived to solve such problem. Since KAM theory is more efficient in finding quasi-periodic solutions, it was widely applied to the nonlinear beam equations with constant coefficient (see [12,29,30,34,35]).…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions of a semilinear Euler-Bernoulli beam equation with variable coefficients

Wei,

2020

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This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described the infinitesimal, free, undamped in-plane bending vibrations of a thin straight elastic beam. When the frequency ω = 2π T is rational, some properties of the beam operator with variable coefficients are investigated. We obtain the existence of periodic solutions when the nonlinear term is monotone and bounded.

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