Boundedness of solutions for semilinear reversible systems

RESONANCE AND NONLINEARITY: A SURVEY REZONANS I NELINIJNIST\: OHLQDThis paper surveys recent results about nonresonant and resonant periodically forced nonlinear oscillators. This includes the existence of periodic, unbounded or bounded solutions for bounded nonlinear perturbations of linear and of piecewise linear oscillators, as well as of some classes of planar Hamiltonian systems.Navedeno ohlqd ostannix rezul\tativ wodo nerezonansnyx i rezonansnyx periodyçno zbudΩuvanyx nelinijnyx oscylqtoriv: isnuvannq periodyçnyx neobmeΩenyx abo obmeΩenyx rozv'qzkivdlq obmeΩenyx nelinijnyx zburen\ linijnyx ta kuskovo-linijnyx oscylqtoriv, a takoΩ deqkyx klasiv ploskyx hamil\-tonovyx system.

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Periodic and unbounded motions in asymmetric oscillators at resonance

2015

Journal of Mathematical Analysis and Applications

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We consider the existence of periodic and unbounded solutions for the asymmetric oscillatorwhere x + = max{x, 0}, x − = max{−x, 0}, a and b are two positive constants, p(t) is a 2π-periodic smooth function and g(x) satisfies lim |x|→+∞ x −1 g(x) = 0. We have proved previously that the boundedness of all the solutions and the existence of unbounded solutions have a close relation to the interaction of some well-defined functions Φ p (θ) and Λ(h). In this paper, we consider some critical cases and obtain some new sufficient conditions for the existence of 2π-periodic and unbounded solutions. In particular, the obtained periodic solutions are new and cannot be deduced from Landesman-Lazer's and Fabry-Fonda's existence conditions. In contrast with many existing results, the function g(x) may be unbounded or oscillatory without asymptotic limits.

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Boundedness of solutions for semilinear reversible systems

Cited by 3 publications

References 17 publications

Bounded and Unbounded Motions in Asymmetric Oscillators at Resonance

Bounded and Unbounded Motions in Asymmetric Oscillators at Resonance

Resonance and nonlinearity: A survey

Periodic and unbounded motions in asymmetric oscillators at resonance

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