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Journal of Inequalities and Applications

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Open Access 01.12.2006 | Research Article

Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part

verfasst von: Andrei Borisovich, Wacław Marzantowicz

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006

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Abstract

We study nonlinear ODE problems in the complex Euclidean space, with the right-hand side being polynomial with nonconstant periodic coefficients. As the coefficients functions, we admit only functions with vanishing Fourier coefficients for negative indices. This leads to an existence theorem which relates the number of solutions with the number of zeros of the averaged right-hand side polynomial. A priori estimates of the norms of solutions are based on the Wirtinger-Poincaré-type inequality. The proof of existence theorem is based on the continuation method of Krasnosielski et al., Mawhin et al., and the Leray-Schauder degree. We give a few applications on the complex Riccati equation and some others.

Vorheriger Artikel Oscillation and nonoscillation theorems for a class of even-order quasilinear functional differential equations

Nächster Artikel Inequalities involving the mean and the standard deviation of nonnegative real numbers

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Titel: Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part
verfasst von: Andrei Borisovich
Wacław Marzantowicz
Publikationsdatum: 01.12.2006
Verlag: Springer International Publishing
Erschienen in: Journal of Inequalities and Applications / Ausgabe 1/2006
Elektronische ISSN: 1029-242X
DOI: https://doi.org/10.1155/JIA/2006/42908

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