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Tytuł artykułu

Existence of solutions for second order stochastic differential inclusions in Hilbert spaces

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Abstrakty

EN
In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.

Twórcy

  • Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram - 624 302, Tamil Nadu, India
autor
  • Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Bibliografia

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  • [4] P. Balasubramaniam, S.K. Ntouyas and D. Vinayagam, Existence of solutions of nonlinear stochastic differential inclusions in a Hilbert space, Comm. Appl. Nonlinear Anal. 12 (2005), 1-15.
  • [5] P. Balasubramaniam and J.Y. Park, Nonlocal Cauchy problem for second order stochastic evolution equations in Hilbert spaces, Dynamic Syst. Appl. (in press).
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  • [8] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
  • [9] W.E. Fitzgibbon, Global existence and boundedness of solutions to the extensible beam equation, SIAM J. Math. Anal. 13 (1982), 739-745.
  • [10] K. Deimling, Multivalued Differential Equations, de Gruyter, New York, 1992.
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  • [12] S. Hu and N.S. Papageorgiou, On the existence of periodic solutions for non-convex valued differential inclusions in ℝⁿ, Proc. Amer. Math. Soc. 123 (1995), 3043-3050.
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  • [17] N.I. Mahmudov and M.A. McKibben, Abstract second-order damped McKean-Vlasov stochastic evolution equations, Stochastic Anal. Appl. 24 (2006), 303-328.
  • [18] M.A. McKibben, Second-order neutral stochastic evolution equations with heredity, J. Appl. Math. Stochastic Anal. 2 (2004), 177-192.
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  • [20] M. Martelli, A Rothe's type theorem for non-compact acyclic-valued map, Boll. Unione Mat. Ital. 4 (11) (1975), 70-76.
  • [21] S.K. Ntouyas, Global existence results for certain second order delay integrodifferential equations with nonlocal conditions, Dynam. Systems Appl. 7 (1998), 415-425.
  • [22] S.K. Ntouyas and P.Ch. Tsamatos, Global existence for second order functional semilinear equations, Period. Math. Hungar. 31 (1995), 223-228.
  • [23] N. Papageorgiou, Boundary value problems for evolution inclusions, Comment. Math. Univ. Carol. 29 (1988), 355-362.
  • [24] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983.
  • [25] R. Pettersson, Yosida approximations for multivalued stochastic differential equations, Stochastics and Stochastics Reports 52 (1995), 107-120.
  • [26] R. Pettersson, Existence theorem and Wong-Zakai approximations for multivalued stochastic differential equations, Probability and Mathematical Statistics 17 (1997), 29-45.
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  • [29] C.C. Travis and G.F. Webb, An abstract second order semilinear Volterra integrodifferential equation, SIAM J. Math. Anal. 10 (1979), 412-424.

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Bibliografia

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