RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES AND HENSTOCK-KURZWEIL-PETTIS INTEGRALS.
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| Title: | RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES AND HENSTOCK-KURZWEIL-PETTIS INTEGRALS. |
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| Authors: | Sikorska-Nowak, A.1 anetas@amu.edu.pl |
| Source: | Discussiones Mathematicae: Differential Inclusions, Control & Optimization. 2007, Vol. 27 Issue 2, p315-327. 13p. |
| Subjects: | Banach spaces, Integral theorems, Mathematical variables, Differential equations, Mathematics education |
| Abstract: | We prove an existence theorem for the equation x′ = f(t, xt) x(ϴ) = φ(ϴ), where xt(ϴ) = x(t + ϴ), for -r ≤ ϴ < 0, t ϵ Ia, Ia = [0, a] a ϵ R+ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness. [ABSTRACT FROM AUTHOR] |
| Copyright of Discussiones Mathematicae: Differential Inclusions, Control & Optimization is the property of Discussiones Mathematicae Differential Inclusions, Control & Optimization and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 35841653 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES AND HENSTOCK-KURZWEIL-PETTIS INTEGRALS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Sikorska-Nowak%2C+A%2E%22">Sikorska-Nowak, A.</searchLink><relatesTo>1</relatesTo><i> anetas@amu.edu.pl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discussiones+Mathematicae%3A+Differential+Inclusions%2C+Control+%26+Optimization%22">Discussiones Mathematicae: Differential Inclusions, Control & Optimization</searchLink>. 2007, Vol. 27 Issue 2, p315-327. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Banach+spaces%22">Banach spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+theorems%22">Integral theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+variables%22">Mathematical variables</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+education%22">Mathematics education</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We prove an existence theorem for the equation x′ = f(t, xt) x(ϴ) = φ(ϴ), where xt(ϴ) = x(t + ϴ), for -r ≤ ϴ < 0, t ϵ Ia, Ia = [0, a] a ϵ R+ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discussiones Mathematicae: Differential Inclusions, Control & Optimization is the property of Discussiones Mathematicae Differential Inclusions, Control & Optimization and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.7151/dmdico.1087 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 315 Subjects: – SubjectFull: Banach spaces Type: general – SubjectFull: Integral theorems Type: general – SubjectFull: Mathematical variables Type: general – SubjectFull: Differential equations Type: general – SubjectFull: Mathematics education Type: general Titles: – TitleFull: RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES AND HENSTOCK-KURZWEIL-PETTIS INTEGRALS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Sikorska-Nowak, A. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: 2007 Type: published Y: 2007 Identifiers: – Type: issn-print Value: 15099407 Numbering: – Type: volume Value: 27 – Type: issue Value: 2 Titles: – TitleFull: Discussiones Mathematicae: Differential Inclusions, Control & Optimization Type: main |
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