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Existence Result for Stochastic Impulsive Differential Inclusions


M. O. Ogundiran

Department of Mathematics,
Obafemi Awolowo University,
Ile-Ife. Nigeria


We establish the existence of solution of Stochastic impulsive differential inclusion in infinite dimensional space. We employed fixed point theorem for multivalued map to obtain the solution.


  1. Ahmed, N. U. Non linear stochastic differential inclusions on Banach space, Stoch. Anal. Appl. 12, (1994), 1-10
  2. Aubin , J. P. and Cellina, A. Differential Inclusions, Springer- Verlag, Berlin, 1984
  3. Benchohra, M. , Henderson, J. and Ntouyas, S. K. Impulsive differential equations and inclusions Hindawi Publishing Corporation, vol 2., New York, 2006
  4. Cernea, A. On an Evolution inclusion in non-separable Banach spaces Opuscula Mathematica, 2, 131-138, (2009)
  5. Deimling, K. Multivalued differential equations, Walter de Gruyter, 1992
  6. Es-Sarhir, A. Existence and uniqueness of invariant measures for a class of transition semigroups on Hilbert spaces J. Math. Anal Appl. , 353, 497-507, (2009)
  7. Kisielewicz, M. Stochastic representation of partial differential inclusions J. Math. Anal Appl. , 353, (2009), 592-606
  8. V. Lakshmikantham, V., Bainov, D. D. and Simenov, P. S. Theorem of Impulsive Differential Equations , World Scientific, Singapore, 1989
  9. A. Lasota, A. and Opial, Z. An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys., 13, (1965), 781-786
  10. Michael, E. Continuous selections, I and II, Annals of Math. 63; 64, (1956), 361-382, 562-580
  11. Ning, H. W. and Liu, B. Existence results for impulsive neutral stochastic evolution inclusions in Hilbert space, Acta Math. Sinica, English series 27, 7, (2011), 1405-1418
  12. Pan, L. Existence of mild solution for impulsive stochastic differential equations with nonlocal conditions Diff. Equat. and Appl. 4, 3, (2012), 485-494
  13. Prato, G. D. and Zabczyk, J. Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992
  14. Shen, L. J. and Sun, J. T. Existence and uniqueness of mild solutions for non linear stochastic impulsive differential equation, Abstract and Applied Anal. vol. 2011, ID 439724, (2011), 1-10
  15. E. Zeidler, E. Nonlinear Functional Analysis and Its Applications, I. Fixed-Point Theorems, Springer, New York, 1986.

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