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Journal Articles Boundary Value Problems Year : 2013

Several kinds of oscillations in forced Lienard equations

Abstract

Near an equilibrium we study the existence of asymptotically a.p. (almost periodic), asymptotically a.a. (almost automorphic), pseudo a.p., pseudo a.a., weighed pseudo a. p. and weighed pseudo a. a. solutions of Lienard differential equations in the form x ''(t) + f(x(t),p).x '(t) + g(x(t),p) = e(p)(t), where the forcing term possesses a similar nature, and where p is a parameter in a Banach space. We use a perturbation method around an equilibrium. We also study two special cases of the previous family of equations that are x ''(t) + f(x(t)).x '(t) + g(x(t)) = e(t) and x ''(t) + f(x(t),q).x '(t) + g(x(t),q) = e(t).

Dates and versions

hal-02166379 , version 1 (26-06-2019)

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Joël Blot, Souhila Boudjema, Philippe Cieutat. Several kinds of oscillations in forced Lienard equations. Boundary Value Problems, 2013, ⟨10.1186/1687-2770-2013-66⟩. ⟨hal-02166379⟩
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