Open Access

On the Kneser-Type Solutions for Two-Dimensional Linear Differential Systems with Deviating Arguments

Journal of Inequalities and Applications20072007:052304

DOI: 10.1155/2007/52304

Received: 7 January 2007

Accepted: 25 April 2007

Published: 4 July 2007

Abstract

For the differential system https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq1_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq2_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq3_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq4_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq5_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq6_HTML.gif , we get necessary and sufficient conditions that this system does not have solutions satisfying the condition https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq7_HTML.gif for https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq8_HTML.gif . Note one of our results obtained for this system with constant coefficients and delays ( https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq9_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq10_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq11_HTML.gif ). The inequality https://static-content.springer.com/image/art%3A10.1155%2F2007%2F52304/MediaObjects/13660_2007_Article_1712_IEq12_HTML.gif is necessary and sufficient for nonexistence of solutions satisfying this condition.

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Authors’ Affiliations

(1)
Department of Mathematics and Computer Sciences, The Academic College of Judea and Samaria
(2)
Department of Mathematics, University of Tbilisi

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Copyright

© A. Domoshnitsky and R. Koplatadze. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.