Existence and uniqueness of solutions for random impulsive differential equation

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DOI:

https://doi.org/10.26637/mjm0101/002

Abstract

In this paper, we study the existence and uniqueness of the mild solutions for random impulsive differential equations through fixed point technique. An example is provided to illustrate the theory.

Keywords:

Existence, Uniqueness, Random impulses, Fixed point theorem

Mathematics Subject Classification:

35R12, 60H99, 35B40, 34G20
  • A. Vinodkumar Department of Mathematics, PSG College of Technology, Coimbatore-641 004, Tamil Nadu, India.
  • Pages: 8-13
  • Date Published: 01-09-2012
  • Vol. 1 No. 1 (2012): Inaugural Issue :: Malaya Journal of Matematik (MJM)

A. Anguraj, M. Mallika Arjunan and E. Hernández, Existence results for an impulsive partial neutral functional differential equations with state - dependent delay, Appl. Anal., 86(7)(2007), 861-872. DOI: https://doi.org/10.1080/00036810701354995

A. Anguraj, S. Wu and A. Vinodkumar, Existence and exponential stability of semilinear functional differential equations with random impulses under non-uniqueness, Nonlinear Analysis: Theory, Methods & Applications, 74(2011), 331-342. DOI: https://doi.org/10.1016/j.na.2010.07.007

A. Anguraj and A. Vinodkumar, Existence, uniqueness and stability results of random impulsive semilinear differential systems, Nonlinear Analysis Hybrid Systems, 3(2010), 475-483. DOI: https://doi.org/10.1016/j.nahs.2009.11.004

A. Anguraj and A. Vinodkumar, Existence and uniqueness of neutral functional differential equations with random impulses, International Journal of Nonlinear Science, 8(4)(2009), 412-418.

E. Hernández, M. Rabello, and H. R. Henriquez, Existence of solutions for impulsive partial neutral functional differential equations, J. Math. Anal. Appl., 331(2007)1135-1158. DOI: https://doi.org/10.1016/j.jmaa.2006.09.043

R. Iwankievicz and S. R. K. Nielsen, Dynamic response of non-linear systems to Poisson distributed random impulses, J. Sound Vibration, 156(1992), 407-423. DOI: https://doi.org/10.1016/0022-460X(92)90736-H

V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. DOI: https://doi.org/10.1142/0906

A. M. Samoilenko and N. A Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. DOI: https://doi.org/10.1142/2892

J. M. Sanz-Serna and A. M. Stuart, Ergodicity of dissipative differential equations subject to random impulses, J. Differential Equations, 55(1999), 262-284. DOI: https://doi.org/10.1006/jdeq.1998.3594

K. Tatsuyuki, K. Takashi and S. Satoshi, Drift motion of granules in chara cells induced by random impulses due to the myosinactin interaction, Physica A, 248(1998), 21-27. DOI: https://doi.org/10.1016/S0378-4371(97)00455-X

A. Vinodkumar, Existence results on random impulsive semilinear functional differential inclusions with delays, Ann. Funct. Anal., 3 (2012), 89-106. DOI: https://doi.org/10.15352/afa/1399899934

A. Vinodkumar and A. Anguraj, Existence of random impulsive abstract neutral non-autonomous differential inclusions with delays, Nonlinear Anal. Hybrid Systems, 5(2011), 413426. DOI: https://doi.org/10.1016/j.nahs.2011.04.002

S. J. Wu and X. Z. Meng, Boundedness of nonlinear differential systems with impulsive effect on random moments, Acta Math. Appl. Sin., 20(1)(2004), 147-154. DOI: https://doi.org/10.1007/s10255-004-0157-z

S. J. Wu and Y. R. Duan, Oscillation, stability, and boundedness of second-order differential systems with random impulses, Comput. Math. Appl., 49(9-10)(2005), 1375-1386. DOI: https://doi.org/10.1016/j.camwa.2004.12.009

S. J. Wu, X. L. Guo and S. Q. Lin, Existence and uniqueness of solutions to random impulsive differential systems, Acta Math. Appl. Sin., 22(4)(2006), 595-600. DOI: https://doi.org/10.1007/s10255-006-0336-1

S. J. Wu, X. L. Guo and Y. Zhou, p−moment stability of functional differential equations with random impulses, Comput. Math. Appl., 52(2006), 1683-1694. DOI: https://doi.org/10.1016/j.camwa.2006.04.026

S. J. Wu, X. L. Guo and R. H. Zhai, Almost sure stability of functional differential equations with random impulses, Dyn. Cont. Discre. Impulsive Syst.: Series A, 15(2008), 403-415.

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Published

01-09-2012

How to Cite

A. Vinodkumar. “Existence and Uniqueness of Solutions for Random Impulsive Differential Equation”. Malaya Journal of Matematik, vol. 1, no. 1, Sept. 2012, pp. 8-13, doi:10.26637/mjm0101/002.