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Note to the existence of periodic solutions for higher-order differential equations with nonlinear restoring term and time-variable coefficients. (English) Zbl 0757.34031
The authors state the conditions on $$p(t)$$, $$h(x)$$ and $$a_{ij}(t)$$ which permit to use the Leray-Schauder continuation theorem for proving the existence of an $$\omega$$-periodic solution of the equation $$x^{(n)}+\sum_{j=1}^{n-1} a_ j(t)x^{(n-j)}(t)+h(x)=p(t)$$, $$n=2,3,\dots,8$$.
##### MSC:
 34C25 Periodic solutions to ordinary differential equations
##### Keywords:
periodic solution; Leray-Schauder continuation theorem
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##### References:
 [1] Andres J.: Existence of periodic solutions for an N-th order differential equation with nonlinear restoring term and time-variable coefficients. · Zbl 0762.34017 [2] Fučík S., Mawhin J.: Periodic solutions of some nonlinear differential equation of higher order. Čas. Pěst. Mat. 100 (1975), 276-283. · Zbl 0306.34056 [3] Lasota A., Szafraniec F.H.: Sur les solutions périodique d’une équation différentielle ordinaire d’ordre n. Annal. Polon. Math. 18 (1966), 339-344. · Zbl 0166.08601
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