Voir la notice de l'article provenant de la source Library of Science
@article{DMDICO_2007_27_2_a7,
author = {Balasubramaniam, P. and Ntouyas, S.},
title = {Existence of solutions for second order stochastic differential inclusions in {Hilbert} spaces},
journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization},
pages = {365--384},
publisher = {mathdoc},
volume = {27},
number = {2},
year = {2007},
zbl = {1155.34034},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMDICO_2007_27_2_a7/}
}
TY - JOUR AU - Balasubramaniam, P. AU - Ntouyas, S. TI - Existence of solutions for second order stochastic differential inclusions in Hilbert spaces JO - Discussiones Mathematicae. Differential Inclusions, Control and Optimization PY - 2007 SP - 365 EP - 384 VL - 27 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMDICO_2007_27_2_a7/ LA - en ID - DMDICO_2007_27_2_a7 ER -
%0 Journal Article %A Balasubramaniam, P. %A Ntouyas, S. %T Existence of solutions for second order stochastic differential inclusions in Hilbert spaces %J Discussiones Mathematicae. Differential Inclusions, Control and Optimization %D 2007 %P 365-384 %V 27 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMDICO_2007_27_2_a7/ %G en %F DMDICO_2007_27_2_a7
Balasubramaniam, P.; Ntouyas, S. Existence of solutions for second order stochastic differential inclusions in Hilbert spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 27 (2007) no. 2, pp. 365-384. http://geodesic.mathdoc.fr/item/DMDICO_2007_27_2_a7/
[1] N.U. Ahmed, Nonlinear stochastic differential inclusions on Banach space, Stochastic Anal. Appl. 12 (1994), 1-10.
[2] J.P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984.
[3] P. Balasubramaniam, Existence of solutions of functional stochastic differential inclusions, Tamkang J. Math. 33 (2002), 35-43.
[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).
[6] J. Ball, Initial boundary value problems for an extensible beam, J. Math. Anal. Appl. 42 (1973), 61-90.
[7] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 2 (1991), 155-166.
[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.
[11] A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
[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.
[13] S. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Vol. I. Theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 1997.
[14] D.N. Keck and M.A. McKibben, Functional integro-differential stochastic evolution equations in Hilbert space, J. Appl. Math. Stochastic Anal. 16 (2003), 127-147.
[15] P. Kree, Diffusion equation for multivalued stochastic differential equations, J. Funct. Anal. 49 (1982), 73-90.
[16] A. Lasota and Z. Opial, An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
[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.
[19] M. Michta and J. Motyl, Second order stochastic inclusion, Stochastic Anal. Appl. 22 (2004), 701-720.
[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.
[27] T. Taniguchi, K. Liu and A. Truman, Existence, uniqueness and asymptotic behavior of mild solutions to stochastic functional differential equations in Hilbert spaces, J. Differential Equations 181 (2002), 72-91.
[28] C.C. Travis and G.F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Mathematica Academiae Scientiarum Hungaricae 32 (1978), 75-96.
[29] C.C. Travis and G.F. Webb, An abstract second order semilinear Volterra integrodifferential equation, SIAM J. Math. Anal. 10 (1979), 412-424.