OSCILLATIONS DANS DES ÉQUATIONS DE LIÉNARD ET DES ÉQUATIONS D'ÉVOLUTION SEMI-LINÉAIRES

Abstract : In this work, near an equilibrium, we study the existence, uniqueness and regular dependence of almost periodic (a.p.), almost automorphic (a.a.), asymptotically a.p., asymptotically a.a., pseudo a.p., pseudo a.a., weighed pseudo a.p., weighed pseudo a.a. solutions of Liénard differential equations in the form x''(t) + f(x(t), p). x'(t) + g(x(t), p) = ep(t), (1) where the term ep possesses a similar nature, and where p is a parameter in Banach space. We use a theorem of implicit functions around an equilibrium. We also study two special cases of (1), that are x''(t) + f1(x(t)). x'(t) + g1(x(t))= e(t), x''(t) + f2(x(t), q). x'(t) + g2(x(t), q) = e(t). We establish also, a new result of differentiable dependence on the S-asymptotically almost-periodic solution of a Cauchy problem x'(t)=A(t) x(t)+f(t, x(t),u(t) ) x(0) = ζ. The dependence concerns the initial conditions ζ and control term u. We apply this result to parabolic evolution equation with periodic coefficients in time.
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Submitted on : Monday, November 11, 2013 - 3:37:08 PM
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Souhila Boudjema. OSCILLATIONS DANS DES ÉQUATIONS DE LIÉNARD ET DES ÉQUATIONS D'ÉVOLUTION SEMI-LINÉAIRES. Analyse fonctionnelle [math.FA]. Université Panthéon-Sorbonne - Paris I, 2013. Français. ⟨tel-00903302⟩

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