- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 784638, 17 pages
Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions
1Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore, Tamil Nadu 641 004, India
2Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 5046, Dhabran 31261, Saudi Arabia
Received 31 May 2011; Accepted 6 October 2011
Academic Editor: Jiongmin Yong
Copyright © 2011 A. Vinodkumar and A. Boucherif. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- K. Balachandran and K. Uchiyama, “Existence of solutions of nonlinear integrodifferential equations of Sobolev type with nonlocal condition in Banach spaces,” Proceedings of the Indian Academy of Sciences (Mathematical Sciences), vol. 110, no. 2, pp. 225–232, 2000.
- L. Byszewski, “Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem,” Journal of Mathematical Analysis and Applications, vol. 162, no. 2, pp. 494–505, 1991.
- K. Deng, “Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions,” Journal of Mathematical Analysis and Applications, vol. 179, no. 2, pp. 630–637, 1993.
- M. Benchohra, E. P. Gatsori, J. Henderson, and S. K. Ntouyas, “Nondensely defined evolution impulsive differential inclusions with nonlocal conditions,” Journal of Mathematical Analysis and Applications, vol. 286, no. 1, pp. 307–325, 2003.
- A. Boucherif and R. Precup, “Semilinear evolution equations with nonlocal initial conditions,” Dynamic Systems and Applications, vol. 16, no. 3, pp. 507–516, 2007.
- X. Fu and K. Ezzinbi, “Existence of solutions for neutral functional differential evolution equations with nonlocal conditions,” Nonlinear Analysis, vol. 54, no. 2, pp. 215–227, 2003.
- J. Liang and Ti.-J. Xiao, “Semilinear integrodifferential equations with nonlocal initial conditions,” Computers & Mathematics with Applications, vol. 47, no. 6-7, pp. 863–875, 2004.
- A. Boucherif, “Semilinear evolution inclusions with nonlocal conditions,” Applied Mathematics Letters, vol. 22, no. 8, pp. 1145–1149, 2009.
- N. U. Ahmed, “Nonlinear stochastic differential inclusions on Banach space,” Stochastic Analysis and Applications, vol. 12, no. 1, pp. 1–10, 1994.
- P. Balasubramaniam and S. K. Ntouyas, “Controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space,” Journal of Mathematical Analysis and Applications, vol. 324, no. 1, pp. 161–176, 2006.
- G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, vol. 44, Cambridge University Press, Cambridge, UK, 1992.
- P. Krée, “Diffusion equation for multivalued stochastic differential equations,” Journal of Functional Analysis, vol. 49, no. 1, pp. 73–90, 1982.
- S. Aizicovici and V. Staicu, “Multivalued evolution equations with nonlocal initial conditions in Banach spaces,” Nonlinear Differential Equations and Applications, vol. 14, no. 3-4, pp. 361–376, 2007.
- D. N. Keck and M. A. McKibben, “Functional integro-differential stochastic evolution equations in Hilbert space,” Journal of Applied Mathematics and Stochastic Analysis, vol. 16, no. 2, pp. 141–161, 2003.
- A. Lin and L. Hu, “Existence results for impulsive neutral stochastic functional integro-differential inclusions with nonlocal initial conditions,” Computers & Mathematics with Applications, vol. 59, no. 1, pp. 64–73, 2010.
- A. Elazzouzi and A. Ouhinou, “Optimal regularity and stability analysis in the α-norm for a class of partial functional differential equations with infinite delay,” Discrete and Continuous Dynamical Systems, vol. 30, no. 1, pp. 115–135, 2011.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44, Springer, New York, NY, USA, 1983.
- J.-P. Aubin and A. Cellina, Differential Inclusions, vol. 264, Springer, Berlin, Germany, 1984.
- K. Deimling, Multivalued Differential Equations, vol. 1, Walter de Gruyter, New York, NY, USA, 1992.
- S. Hu and N. S. Papageorgiou, “On the existence of periodic solutions for nonconvex-valued differential inclusions in ,” Proceedings of the American Mathematical Society, vol. 123, no. 10, pp. 3043–3050, 1995.
- A. Granas and J. Dugundji, Fixed Point Theory, Springer, New York, NY, USA, 2003.
- A. Lasota and Z. Opial, “An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations,” Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 13, pp. 781–786, 1965.
- J. Hofbauer and P. L. Simon, “An existence theorem for parabolic equations on with discontinuous nonlinearity,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 8, pp. 1–9, 2001.