Asymptotic Stability of Testable Measure Differential Equations

Benjamin Oyediran Oyelami

doi:https://doi.org/10.14445/22315373/IJMTT-V13P514

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 13 | Number 2 | Year 2014 | Article Id. IJMTT-V13P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V13P514

Asymptotic Stability of Testable Measure Differential Equations

Benjamin Oyediran Oyelami

Citation :

Benjamin Oyediran Oyelami, "Asymptotic Stability of Testable Measure Differential Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 13, no. 2, pp. 97-115, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V13P514

Abstract

In this paper, we consider sufficiency conditions for the stability of trivial solutions of measure differential equations. The bound for in the Pandit's problem is estimated in a systematic way and used to establish criteria for the stability of trivial solutions. Results on asymptotic stability for testable perturbed measure differential equations are obtained using some growth properties, Pandit inequality and Brascamp-Lieb inequality. An example is used to illustrate the application of results obtained.

Keywords

Stability, Testable system, Measure differential equations and impulses.

References

[1] Bellman R. Stability theory of differential equations. McGraw-Hill, New York, 1953.
[2] Codington, E.A. and Levinson. Theory of ordinary differential equations. McGraw-Hill, New York, 1955.
[3] Frank Barthe "The Brunn-Minkowski and functional in equalities" Proceedings of International Congress of Mathematicians Madrid Spain 2006, 1529-1562.
[4] Gurgula, S.I. and Perestyuk, N.A. "Stability of the equilibrium situation in Impulsive System". Mat. Fiz. No. 3 (1982), 9-14, 16.
[5] Jack K. Hale, “Ordinary differential equations”. Wiley-Interscience Vol. xxi, 1969.
[6] Leela, S. "Stability of Measure Differential System with Impulsive perturbation in term of two measures". Nonlinear Anal. 1 (1977), 667-677.
[7] Leela, S. “Stability of Measure Differential Equations Systems”. Pacific J. Math 55 (1974), 489-498.
[8] Mingaralli and Angelo, B. “On a Stieltjes Version of Gronwall's Inequality”. Proc. Amer. Math. Soc. 82 (1981), No. 2, 249-252.
[9] Michel A.M., Farell, J/A. and Porod. “Qualitative analysis of neutral network Information and Decision technologies” Vol. 14, No. 3 (1988), 169-194.
[10] Oyelami, Benjamin Oyediran. “Impulsive system and applications to some models”. Ph.D. Dissertation submitted to the Abubakar Tafawa University, Nigeria,1999.
[11] Oyelami B. O. “Studies in impulsive system and applications”. A monograph, Lambert Academic Publisher Germany, December 8, 2012 .ISBN: 978-3-659-20724-2.
[12] Oyelami B O and Ale S O. “Impulsive Differential Equations and Applications to Some Models: Theory and Applications”. A monograph, Lambert Academic Publisher Germany, March 24, 2012 .ISBN: 978-3-8484-4740-4.
[13] Oyelami Benjamin Oyediran “On military model for impulsive reinforcement functions using marginalization techniques.” Nonlinear Analysis 35,1999, 947-958.
[14] Oyelami B.O. and Ale S.O. (2009) "Boundedness of solutions of a delay impulsive perturbed system". The Proc. Inter. Conference in Memory of C.O.A. Sowunmi, Univ. of Ibadan, Nigeria, Vol. 1, 82-101.
[15] Pandit, S.O. “On the stability of Impulsive perturbed differential systems”. Bull. Astral Math Soc 17 (1977), 423-432.
[16]------------- With Deo S.G. “Differential System Involving Impulsive”. Lecture notes in Mathematics, Springer-Verlag, Berlin, New York, 1982.
[17] Shilov G. E. and Gurevich B.J. ” Integral Measure and Derivative: A Unified Approach”. Prentice Hall. Delhi – Bombay( 1966).
[18] Taylor S. J.”Measure and Integration”. Cambridge University Press. London (1973):.
[19] Treves, Francois “Topological Vector Spaces, Distribution and Kernels”. New York, Academic Press (1967).
[20] Yosida, Kosasa “Functional Analysis” Springer-verlag Berlin. Sixth Edition (1980).