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).
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Submitted on : Wednesday, June 26, 2019 - 5:16:04 PM
Last modification on : Thursday, June 27, 2019 - 1:33:34 AM

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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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