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The Darboux problem involving the distributional Henstock–Kurzweil integral

Part of: Distributions, generalized functions, distribution spaces Real functions Measures, integration, derivative, holomorphy Set functions, measures and integrals with values in abstract spaces

Published online by Cambridge University Press:  04 January 2012

Yueping Lu ,
Guoju Ye ,
Ying Wang  and
Wei Liu
Yueping Lu
Affiliation:
Department of Mathematics, Hohai University, Nanjing 210098, People's Republic of China ([email protected]; [email protected])
Guoju Ye
Affiliation:
Department of Mathematics, Hohai University, Nanjing 210098, People's Republic of China ([email protected]; [email protected])
Ying Wang
Affiliation:
Department of Mathematics, Hohai University, Nanjing 210098, People's Republic of China ([email protected]; [email protected])
Wei Liu
Affiliation:
Department of Mathematics, Hohai University, Nanjing 210098, People's Republic of China ([email protected]; [email protected])
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Abstract

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In this paper, using the Schauder Fixed Point Theorem and the Vidossich Theorem, we study the existence of solutions and the structure of the set of solutions of the Darboux problem involving the distributional Henstock–Kurzweil integral. The two theorems presented in this paper are extensions of the previous results of Deblasi and Myjak and of Bugajewski and Szufla.

Keywords

Henstock–Kurzweil integralSchauder Fixed Point TheoremVidossich TheoremdistributionDarboux problemdistributional Henstock–Kurzweil integral

MSC classification

Secondary: 26A39: Denjoy and Perron integrals, other special integrals 28B05: Vector-valued set functions, measures and integrals 46F05: Topological linear spaces of test functions, distributions and ultradistributions 46G10: Vector-valued measures and integration 46G12: Measures and integration on abstract linear spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 197 - 205
Copyright
Copyright © Edinburgh Mathematical Society 2011

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