Abstract
We consider semilinear difference-delay equations with continuous time in a Euclidean space. Estimates are found for the solutions. Such estimates are then applied to obtain the stability and boundedness criteria for solutions.
Research Article | Open Access
Solution Estimates for Semilinear Difference-Delay Equations with Continuous Time
Received05 Jul 2007
Accepted11 Aug 2007
Published04 Oct 2007
References
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetV. Kolmanovskiĭ and A. Myshkis, Applied Theory of Functional-Differential Equations, vol. 85 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS.-I. Niculescu, Delay Effects on Stability: A Robust Control Approach, vol. 269 of Lecture Notes in Control and Information Sciences, Springer, London, UK, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Pepe, “The Liapunov's second method for continuous time difference equations,” International Journal of Robust and Nonlinear Control, vol. 13, no. 15, pp. 1389–1405, 2003.
View at: Publisher Site | Google Scholar | MathSciNetA. N. Sharkovsky, Yu. L. Maĭstrenko, and E. Yu. Romanenko, Difference Equations and Their Applications, vol. 250 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. S. Cheng and Y.-Z. Lin, “Exact region of stability for an investment plan with three parameters,” Applied Mathematics E-Notes, vol. 5, pp. 194–201, 2005.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. S. Cheng and S. S. Chiou, “Exact stability regions for quartic polynomials,” Bulletin of the Brazilian Mathematical Society, vol. 38, no. 1, pp. 21–38, 2007.
View at: Publisher Site | Google Scholar | MathSciNetM. I. Gil', Difference Equations in Normed Spaces: Stability and Oscillations, vol. 206 of North-Holland, Mathematics Studies, Elsevier, Amsterdam, The Netherlands, 2007.
View at: Google ScholarN. Dunford and J. T. Schwartz, Linear Operators. Part I: General Theory, Interscience, New York, NY, USA, 1966.
View at: Google ScholarM. I. Gil', Operator Functions and Localization of Spectra, vol. 1830 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. I. Gil', “Bounds for characteristic values of entire matrix pencils,” Linear Algebra and Its Applications, vol. 390, no. 1, pp. 311–320, 2004.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. I. Gil', “On variations of characteristic values of entire matrix pencils,” Journal of Approximation Theory, vol. 136, no. 1, pp. 115–128, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetT.-Z. Huang and X.-P. Liu, “Estimations for certain determinants,” Computers & Mathematics with Applications, vol. 50, no. 10–12, pp. 1677–1684, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2007 Michael Gil' and Sui Sun Cheng. 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.