Representation and stability of solutions of systems of functional differential equations with multiple delays
This paper is devoted to the study of systems of nonlinear functional differential equations with time-dependent coefficients and multiple variable increasing delays represented by functions $g_i(t)<t$. The solution is found in terms of a piecewise-defined matrix function. Using our representatio...
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| Format: | Article |
| Language: | English |
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University of Szeged
2012-08-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1660 |
| Summary: | This paper is devoted to the study of systems of nonlinear functional differential equations with time-dependent coefficients and multiple variable increasing delays represented by functions $g_i(t)<t$. The solution is found in terms of a piecewise-defined matrix function. Using our representation of the solution and Gronwall's, Bihari's and Pinto's integral inequalities, asymptotic stability results are proved for some classes of nonlinear functional differential equations with multiple variable delays and linear parts given by pairwise permutable constant matrices. The derived theory is illustrated on nontrivial examples. |
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| ISSN: | 1417-3875 |