Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

SOLVABILITY OF IMPULSIVE NEUTRAL FUNCTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS WITH STATE DEPENDENT DELAY

  • Karthikeyan, K. (Department of Mathematics, KSR College of Technology) ;
  • Anguraj, A. (Department of Mathematics, PSG College of Arts and Science)
  • 투고 : 2011.02.21
  • 심사 : 2011.06.23
  • 발행 : 2012.01.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.

키워드

참고문헌

  1. A.Anguraj, K.Karthikeyan, Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions, Nonlinear Analysis 70 (2009) 2717-2721. https://doi.org/10.1016/j.na.2008.03.059
  2. A.Anguraj, K.Karthikeyan, Solvability of Impulsive Neutral Integrodifferential Inclusions with Nonlocal Initial Conditions via Fractional Operators, International Journal of Computational and Applied mathematics, Volume 5, Number 4 (2010), pp. 555-571.
  3. A. Anguraj, M.Mallika Arjunan, E. Hermandez M., Existence results for an impulsive neutral functional differential equation with state dependent delay, Appl. Anal. 86(2007) 861-872. https://doi.org/10.1080/00036810701354995
  4. J. Banas and K. Goebel (1980), Measure of Noncompactness in Banach Spaces. Marcel Dekker, New York.
  5. M.Benchohra, J.Henderson, S.K.Ntouyas, Impulsive differential equations and inclusions, Hindawi publishing corporation, Newyork , 2006
  6. Y.K.Chang, A.Anguraj and K.Karthikeyan, Solvability Of Impulsive Evolution Differential Inclusions With Nonlocal Conditions in Banach Space J. Appl. Math. Vol. 27 (2009), No. 5-6, pp. 1235-1246.
  7. Y.K.Chang, A.Anguraj, M.Mallika Arjunan, Existence results for an impulsive neutral functional differential equations with infinite delay, Non linerar Anal. Hybrid syst. 2 (2008) 209-218. https://doi.org/10.1016/j.nahs.2007.10.001
  8. Y.K.Chang, W.T.Li, Existence results for second order impulsive functional differential inclusions, J.Math. Anal. Appl. 301 (2005) 477-490. https://doi.org/10.1016/j.jmaa.2004.07.041
  9. Y.K.Chang and J.J.Nieto, Existence of solutions for impulsive neutral integrodifferential inclusions with non logal initial conditions via fractional operators, Nume. Func. Anal. Opti. 30 [3-4]; 227-244, 2009. https://doi.org/10.1080/01630560902841146
  10. Y.K.Chang, J.J.Nieto, and Z.H.Zhao, Existence results for a non densely-defined impulsive neutral differential equation with state dependent delay, Non linear Anal. Hybrid systems, 4 (2010) 593-599. https://doi.org/10.1016/j.nahs.2010.03.006
  11. K.Deimling, Multi valued differential equation , De Gruyter, Berlin, 1992.
  12. X.Fu, K.Ezzinbi, Existence of solutions for neutral functional differential evaluation equations with non local conditions, Non linear Anal.54 (2003) 215-227. https://doi.org/10.1016/S0362-546X(03)00047-6
  13. R.Grimmer(1982), Resolvent operators for integral equations in banach space. Trans. Am. Math. Soc. 273. 333-349. https://doi.org/10.1090/S0002-9947-1982-0664046-4
  14. R. Grimmer and A.J. Pritchard (1983). Analytic resolvent operators for integral equations in a Banach space. J. Differential Equations 50 : 234-259. https://doi.org/10.1016/0022-0396(83)90076-1
  15. W.M.Haddad, V.Chellabonia, S.G.Nersesov, G.Sergey, Impulsive and hybrid dynamical system, stability, dissipatvity and control Princeton University press, Princeton, NJ, 2006.
  16. E.Hernandez, Existence results for partial neutral integro differential equations with unbounded delay , J.Math.Anal.Appl.29 2 (2004) 194-210.
  17. E.Hernandez, M.A.Mckibben, On state dependent delay partial neutral functional differential equations, Appl.Math.comp.186 (2007) 294-301. https://doi.org/10.1016/j.amc.2006.07.103
  18. E.Hernandez, M.Pierri, G.Goncal ves, Existence results for an impulsive abstract partial differential equation with state dependent delay , Comp.Math.Appl.52 (2006) 411-420. https://doi.org/10.1016/j.camwa.2006.03.022
  19. E.Hernandez, R.Sakthivel, S.Tanaka A.Ki, Existence results for impulsive evolution differential equation with state dependent delay, Electro.J.Differential equation 28 (2008) 1-11.
  20. S. Hu and N. Papageorgiou (1997). Handbook of Multivalued Analysis, Volume 1: Theory. Kluwer, Dordrecht.
  21. V.Lakshmikantham, D.D.Bainov, P.S.Simeonov, Theory of impulsive differential equations world scientific, Singapore-1989.
  22. A.Lasota, Z.Opial, An application of the kakutani-ky Fan theorem in the theory of ordinary differential equation, Bull.Acad.Polon.Sci.Ser.Sci.Math.Astrono.Phys. 13 (1965) 781-786.
  23. J.Li, J.J.Nieto, J.Shen, Impulsive periodic boundary value problems of first order differential equations,J.Math.Anal.Appl.325 (2007) 226-236. https://doi.org/10.1016/j.jmaa.2005.04.005
  24. Z.Luo, J.J.Nieto, J.Shen, Anti periodic boundary value problems for first order impulsive ordinary differential equations, Comput.Math.Appl.49 (2005) 253-261. https://doi.org/10.1016/j.camwa.2004.08.010
  25. S.Migorski, A.Ochal, Non linear impulsive evolution inclusions of second order, Dynam.System.Appl. 16 (2007) 155-173.
  26. Wen-Sheng Li, Y.k.Chang, J.J.Nieto, Solvability of impulsive neutral evolution differential inclusions with state dependent delay, Math.comp.Modell. 49 (2009) 1920-1927. https://doi.org/10.1016/j.mcm.2008.12.010
  27. Z.Yang, J.Cao, Existence of periodic solutions in neutral state dependent delayed equations and models, J.Comput.Appl.Math.174(1) (2005) 179-199. https://doi.org/10.1016/j.cam.2004.04.007
  28. K.Yosida, Functional analysis, 6th ed., Springer-Verlag,Berlin,1980.
  29. Wen-Sheng Li, Y.k.Chang, J.J.Nieto, Solvability of impulsive neutral evolution differential inclusions with state dependent delay, Math.comp.Modell. 49 (2009) 1920-1927. https://doi.org/10.1016/j.mcm.2008.12.010
  30. Z.Yang, J.Cao, Existence of periodic solutions in neutral state dependent delayed equations and models, J