Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations
<p/> <p>We obtain the maximum principles for the first-order neutral functional differential equation <inline-formula> <graphic file="1029-242X-2009-141959-i1.gif"/></inline-formula><inline-formula> <graphic file="1029-242X-2009-141959-i2.gif&quo...
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doaj-00d10501187646fcb808b012ddb269612020-11-25T02:30:07ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-01-0120091141959Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential EquationsDomoshnitsky AlexanderMaghakyan AbrahamShklyar Roman<p/> <p>We obtain the maximum principles for the first-order neutral functional differential equation <inline-formula> <graphic file="1029-242X-2009-141959-i1.gif"/></inline-formula><inline-formula> <graphic file="1029-242X-2009-141959-i2.gif"/></inline-formula> where <inline-formula> <graphic file="1029-242X-2009-141959-i3.gif"/></inline-formula><inline-formula> <graphic file="1029-242X-2009-141959-i4.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2009-141959-i5.gif"/></inline-formula> are linear continuous operators, <inline-formula> <graphic file="1029-242X-2009-141959-i6.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-141959-i7.gif"/></inline-formula> are positive operators, <inline-formula> <graphic file="1029-242X-2009-141959-i8.gif"/></inline-formula> is the space of continuous functions, and <inline-formula> <graphic file="1029-242X-2009-141959-i9.gif"/></inline-formula> is the space of essentially bounded functions defined on <inline-formula> <graphic file="1029-242X-2009-141959-i10.gif"/></inline-formula>. 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.</p>http://www.journalofinequalitiesandapplications.com/content/2009/141959 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Domoshnitsky Alexander Maghakyan Abraham Shklyar Roman |
spellingShingle |
Domoshnitsky Alexander Maghakyan Abraham Shklyar Roman Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations Journal of Inequalities and Applications |
author_facet |
Domoshnitsky Alexander Maghakyan Abraham Shklyar Roman |
author_sort |
Domoshnitsky Alexander |
title |
Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations |
title_short |
Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations |
title_full |
Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations |
title_fullStr |
Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations |
title_full_unstemmed |
Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations |
title_sort |
maximum principles and boundary value problems for first-order neutral functional differential equations |
publisher |
SpringerOpen |
series |
Journal of Inequalities and Applications |
issn |
1025-5834 1029-242X |
publishDate |
2009-01-01 |
description |
<p/> <p>We obtain the maximum principles for the first-order neutral functional differential equation <inline-formula> <graphic file="1029-242X-2009-141959-i1.gif"/></inline-formula><inline-formula> <graphic file="1029-242X-2009-141959-i2.gif"/></inline-formula> where <inline-formula> <graphic file="1029-242X-2009-141959-i3.gif"/></inline-formula><inline-formula> <graphic file="1029-242X-2009-141959-i4.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2009-141959-i5.gif"/></inline-formula> are linear continuous operators, <inline-formula> <graphic file="1029-242X-2009-141959-i6.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-141959-i7.gif"/></inline-formula> are positive operators, <inline-formula> <graphic file="1029-242X-2009-141959-i8.gif"/></inline-formula> is the space of continuous functions, and <inline-formula> <graphic file="1029-242X-2009-141959-i9.gif"/></inline-formula> is the space of essentially bounded functions defined on <inline-formula> <graphic file="1029-242X-2009-141959-i10.gif"/></inline-formula>. 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.</p> |
url |
http://www.journalofinequalitiesandapplications.com/content/2009/141959 |
work_keys_str_mv |
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