Functional integro-differential stochastic evolution equations in Hilbert space

Journal of Applied Mathematics and Stochastic Analysis

Volumn 16, Issue 2, 2003, Pages 141-161

  Keck, David N ^a   McKibben, Mark A ^b  

^a OHIO UNIVERSITY   (United States)

^b GOUCHER COLLEGE   (United States)

Author keywords

Probability measure; Semi group; Stochastic evolution equations; Wiener process

Indexed keywords

EID: 34548666696     PISSN: 10489533     EISSN: 16872177     Source Type: Journal    
DOI: 10.1155/S1048953303000108     Document Type: Article

References (34)

1. Ahmed, N.U., Differential inclusions on Banach spaces with nonlocal state constraints, Nonlinear Funct. Anal. & Appl. 6:3 (2001), 395-409.
2. Aizicovici, S. and Gao, Y., Functional differential equations with nonlocal initial conditions, J. Appl. Math. Stochastic Anal. 10 (1997), 145-156.
3. Aizicovici, S. and Hannsgen, K.B., Local existence for abstract semilinear Volterra integrodifferential equations, J. Integral Eqns. Appl. 5:3 (1993), 299-313.
4. Aizicovici, S. and McKibben, M., Existence results for a class of abstract nonlocal Cauchy problems, Nonlinear Anal. 39:5 (2000), 649-668.
5. Aizicovici, S. and McKibben, M., Semilinear Volterra integrodifferential equations with nonlocal initial conditions, Abstract & Appl. Anal. 4:2 (1999), 127-139.
6. Altman, M., Contractors and Contractor Directions, Theory and Applications, Marcel-Dekker, New York 1978.
7. Balasubramaniam, P. and Ntouyas, S.K., Global existence for semilinear stochastic delay evolution equations with nonlocal conditions, Soochow Jour. of Math. 27:3 (July 2001), 331-342.
8. Barbu, V., Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden 1976.
9. Bergström, H., Weak Convergence of Measures, Academic Press, New York 1982.
10. Bharucha-Reid, A.T., Random Integral Equations, Academic Press, New York 1972.
11. Billingsley, P., Weak Convergence of Measures: Applications in Probability, SIAM, Bristol 1971.
12. Breiman, L., Probability, SIAM, Philadelphia 1992.
13. Byszewski, L., Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. & Appl. 162 (1991), 494-505.
14. DaPrato, G. and Zabczyk, J., Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge 1992.
15. Dunford, N. and Schwarz, J.T., Linear Operators, Part I, Wiley Interscience, New York 1958.
16. Govindan, T.E., Autonomous semilinear stochastic Volterra integrodifferential equations in Hilbert spaces, Dyn. Sys. Appl. 3 (1994), 51-74.
17. Govindan, T.E. and Joshi, M.C., Stability and optimal control of stochastic functional differential equations with memory, Numer. Func. Anal. Optim. 13 (1992), 249-265.
18. Govindan, T.E., Stability of stochastic differential equations in a Banach space, In: Mathematical Theory of Control Lecture Notes in Pure and Applied Mathematics 142, Marcel-Dekker, New York 1992.
19. Grecksch, W. and Tudor, C., Stochastic Evolution Equations: A Hilbert Space Approach, Akademie Verlag, Berlin 1995.
20. Ichikawa, A., Stability of semilinear evolution equations, J. Math. Anal. Appl. 90 (1982), 12-44.
21. Jackson, D., Existence and uniqueness of solutions to semilinear nonlocal parabolic equations, J. Math. Anal. Appl. 172 (1993), 256-265.
22. Kannan, D. and Bharucha-Reid, A.T., On a stochastic integrodifferential evolution equation of Volterra type, J. Integral Equations 10 (1985), 351-379.
23. Kunita, H., Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, United Kingdom 1990.
24. Leray, J. and Schauder, J., Topologie et equation fonctionelles, Ann. Sci. Ecole Norm. Sys. 51 (1934), 45-78.
25. Lin, Y.P. and Liu, J.H., Semilinear integrodifferential equations with nonlocal Cauchy problems, Nonlinear Anal. 26:5, (1996), 1023-1033.
26. Londen, S.O. and Nohel, J.A., Nonlinear Volterra integrodifferential equation occurring in heat flow, J. Integral Equations 6 (1984), 11-50.
27. Ntouyas, S.K. and Tsamatos, P.Ch., Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. 210 (1997), 679-687.
28. Ntouyas, S.K. and Tsamatos, P.Ch., Global existence for semilinear evolution integrodifferential equations with delay and nonlocal conditions, Appl. Anal. 64 (1997), 99-105.
29. McKibben, M., Existence Results for Nonlinear Functional Differential Equations, Ph.D. dissertation, Ohio University, Athens, OH 1999.
30. Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York 1983.
31. Schaefer, H., Über die methode der a priori shranken, Math. Annal. 129 (1955), 415-416.
32. Sobczyk, K., Stochastic Differential Equations with Applications to Physics and Engineering, Klüwer Academic Publishers, London 1991.
33. Ward, J.R., Boundary value problems for differential equations in Banach space, J. Math. Anal. Appl. 70 (1979), 589-598.
34. Zeidler, E., Nonlinear Functional Analysis and its Applications II/B: Nonlinear Monotone Operators, Springer, New York 1990.