Commenced in January 2007
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Existence of Solution of Nonlinear Second Order Neutral Stochastic Differential Inclusions with Infinite Delay
Authors: Yong Li
Abstract:
The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps.
Keywords: Mild solution, Convex multivalued map, Neutral stochastic differential inclusions.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337439
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[1] Da Prato, Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
[2] Taniguchi, Successive approximations to solutions of stochastic differential equations, J.Differential Equations 96(1992), 152-169.
[3] R.Pettersson, Yosida approximations for multivalued stochastic differential equations, Stochastics Stochastics Rep. 52(1995), 107-120.
[4] M.Benchohra, S.K Ntouyas, Nonlocal Cauchy Problems for Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces, Journal of Mathematical Analysis and Applications, 258(2), 2001, 573-590.
[5] M.Benchohra, J. Henderson, S.K Ntouyas, Existence Results for Impulsive Multivalued Semilinear Neutral Functional Differential Inclusions in Banach Spaces, J. Math. Anal. Appl. 285(2003)37-49.
[6] P. Balasubramaniam, Existence of solution of functional stochastic differential inclusions, Tamkang Journal Of Mathematics, 33(2002),35-43.
[7] P. Balasubramaniam and D. Vinayagam, Existence of solutions of nonlinear neutral stochastic differential inclusions in a Hilbert space, Stochastic Analysis and Applications, 23(2005),137-151.
[8] J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New York, 1996.
[9] M. Martelli, A Rothe’s type theorem for noncompact acyclic-valued map, Boll.Un.Mat.Ital. 11:(3)(1975), 70-76.
[10] K. Deimling, Multivalued Differential Equations, de Gruyter, Berlin, New York,1992.
[11] S. Hu, N.Papageorgiou, Handbook of Multivalued Analysis, Theory, vol. 1, Kluwer Academic, Dordrecht, Boston, London, 1997.
[12] J. K. Goldstein, Semigroups of Linear Operators and Applications Oxford University Press, New York, NY, 1985.
[13] O. Fattorini, Ordinary differential equations in linear topological spaces I, J.Diff. Eqs.5(1968), 72-105.
[14] O. Fattorini, Ordinary differential equations in linear topological spaces II, J.Diff. Eqs.6(1969), 50-70.
[15] C. C. Travis and G. F. Webb, Cosine families and abstract nonlinear second-order differential equations, Acta. Math. Hungarica, 32 (1978), 75-96.
[16] C. C. Travis and G. F. Webb, Second-Order Differential Equations in Banach Spaces, Proceedings of the International Symposium on Nonlinear Equations in Abstract Spaces, Academic Press, Now York, Ny, pp. 331-361,1978.
[17] A. Lasota, and Z. Optal, Application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations or noncompact acyclic-valued map, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13(1965), 781-786.