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Journal of Inequalities and Applications

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Open Access 01-12-2009 | Research Article

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

Authors: Alexander Domoshnitsky, Abraham Maghakyan, Roman Shklyar

Published in: Journal of Inequalities and Applications | Issue 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.

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Title: Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations
Authors: Alexander Domoshnitsky
Abraham Maghakyan
Roman Shklyar
Publication date: 01-12-2009
Publisher: Springer International Publishing
Published in: Journal of Inequalities and Applications / Issue 1/2009
Electronic ISSN: 1029-242X
DOI: https://doi.org/10.1155/2009/141959

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