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

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

<p/> <p>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 exis...

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Main Authors: Marzantowicz Wac&#322;aw, Borisovich Andrei
Format: Article
Language:English
Published: SpringerOpen 2006-01-01
Series:Journal of Inequalities and Applications
Online Access:http://www.journalofinequalitiesandapplications.com/content/2006/42908
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spelling doaj-93b1ce344c4f42628a976b432ef5e0cd2020-11-25T02:00:58ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2006-01-012006142908Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear partMarzantowicz Wac&#322;awBorisovich Andrei<p/> <p>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-Poincar&#233;-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.</p>http://www.journalofinequalitiesandapplications.com/content/2006/42908
collection DOAJ
language English
format Article
sources DOAJ
author Marzantowicz Wac&#322;aw
Borisovich Andrei
spellingShingle Marzantowicz Wac&#322;aw
Borisovich Andrei
Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part
Journal of Inequalities and Applications
author_facet Marzantowicz Wac&#322;aw
Borisovich Andrei
author_sort Marzantowicz Wac&#322;aw
title Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part
title_short Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part
title_full Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part
title_fullStr Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part
title_full_unstemmed Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part
title_sort positive oriented periodic solutions of the first-order complex ode with polynomial nonlinear part
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1025-5834
1029-242X
publishDate 2006-01-01
description <p/> <p>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-Poincar&#233;-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.</p>
url http://www.journalofinequalitiesandapplications.com/content/2006/42908
work_keys_str_mv AT marzantowiczwac322aw positiveorientedperiodicsolutionsofthefirstordercomplexodewithpolynomialnonlinearpart
AT borisovichandrei positiveorientedperiodicsolutionsofthefirstordercomplexodewithpolynomialnonlinearpart
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