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Journal of Inequalities and Applications

Erschienen in:

Open Access 01.12.2009 | Research Article

Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations

verfasst von: Alexander Domoshnitsky, Abraham Maghakyan, Roman Shklyar

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2009

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Abstract

We obtain the maximum principles for the first-order neutral functional differential equation

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq1_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq2_HTML.gif

where

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq3_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq4_HTML.gif

, and

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq5_HTML.gif

are linear continuous operators,

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq6_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq7_HTML.gif

are positive operators,

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq8_HTML.gif

is the space of continuous functions, and

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq9_HTML.gif

is the space of essentially bounded functions defined on

https://static-content.springer.com/image/art%3A10.1155%2F2009%2F141959/MediaObjects/13660_2009_Article_1894_IEq10_HTML.gif

. New tests on positivity of the Cauchy function and its derivative are proposed. Results on existence and uniqueness of solutions for various boundary value problems are obtained on the basis of the maximum principles.

Vorheriger Artikel On Pečarić-Rajić-Dragomir-Type Inequalities in Normed Linear Spaces

Nächster Artikel Inclusion Properties for Certain Classes of Meromorphic Functions Associated with a Family of Linear Operators

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Titel: Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations
verfasst von: Alexander Domoshnitsky
Abraham Maghakyan
Roman Shklyar
Publikationsdatum: 01.12.2009
Verlag: Springer International Publishing
Erschienen in: Journal of Inequalities and Applications / Ausgabe 1/2009
Elektronische ISSN: 1029-242X
DOI: https://doi.org/10.1155/2009/141959

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