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Periodic solutions of some forced Liénard differential equations at resonance. (English) Zbl 0537.34037

L’A. examine, dans les conditions convenables, l’équation de Liénard \[ (1)\quad x''(t)+f(x(t)),x'(t)+g(t,x(t))=e(t),\quad t\in [0,2\pi], \] lorsque \(x(0)-x(2\pi)=x'(0)-x'(2\pi)=0\). On obtient, comme des cas particuliers, certains résultats de Lazer, Reissig, Martelli, Chang, Gupta etc.
Puis, avec le deuxième théorème, on minimise le nombre des conditions suffisantes, par rapport à l’existence des solutions de l’équation (1) - dans les relations aux limites, notées ci-dessus.
Reviewer: S.Manolov

MSC:

34C25 Periodic solutions to ordinary differential equations
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References:

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