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ON PERIODIC SOLUTIONS FOR FIRST-ORDER DIFFERENTIAL EQUATIONS INVOLVING THE DISTRIBUTIONAL HENSTOCK–KURZWEIL INTEGRAL

Part of: Difference and functional equations Difference equations Measures, integration, derivative, holomorphy Real functions Distributions, generalized functions, distribution spaces

Published online by Cambridge University Press:  06 February 2012

WEI LIU ,
GUOJU YE ,
YING WANG  and
XUEYUAN ZHOU
WEI LIU*
Affiliation:
Department of Mathematics, Hohai University, Nanjing 210098, PR China (email: liuw626@hhu.edu.cn)
GUOJU YE
Affiliation:
Department of Mathematics, Hohai University, Nanjing 210098, PR China (email: yegj@hhu.edu.cn)
YING WANG
Affiliation:
Department of Mathematics, Hohai University, Nanjing 210098, PR China
XUEYUAN ZHOU
Affiliation:
Department of Mathematics, Hohai University, Nanjing 210098, PR China
*
✉For correspondence; e-mail: liuw626@hhu.edu.cn
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Abstract

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The purpose of this paper is to study the existence of periodic solutions and the topological structure of the solution set of first-order differential equations involving the distributional Henstock–Kurzweil integral. The distributional Henstock–Kurzweil integral is a general integral, which includes the Lebesgue and Henstock–Kurzweil integrals. The main results extend some previously known results in the literature.

Keywords

periodic boundary value problemdistributional Henstock–Kurzweil integraldistributional derivativeextremal solutionsfixed point

MSC classification

Secondary: 26A39: Denjoy and Perron integrals, other special integrals 39A23: Periodic solutions 46F05: Topological linear spaces of test functions, distributions and ultradistributions 46G12: Measures and integration on abstract linear spaces

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 2 , October 2012 , pp. 327 - 338
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

Supported by NNSF of China (10871059) and the Fundamental Research Funds for the Central Universities.

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