- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- 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
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 913809, 11 pages
Existence of Solutions for Nonlinear Mixed Type Integrodifferential Functional Evolution Equations with Nonlocal Conditions
Department of Mathematics and Physics, Anhui University of Architecture, Anhui, Hefei 230022, China
Received 29 June 2012; Revised 14 August 2012; Accepted 1 September 2012
Academic Editor: Beata Rzepka
Copyright © 2012 Shengli Xie. 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.
- R. Ravi Kumar, “Nonlocal Cauchy problem for analytic resolvent integrodifferential equations in Banach spaces,” Applied Mathematics and Computation, vol. 204, no. 1, pp. 352–362, 2008.
- B. Radhakrishnan and K. Balachandran, “Controllability results for semilinear impulsive integrodifferential evolution systems with nonlocal conditions,” Journal of Control Theory and Applications, vol. 10, no. 1, pp. 28–34, 2012.
- J. Wang and W. Wei, “A class of nonlocal impulsive problems for integrodifferential equations in Banach spaces,” Results in Mathematics, vol. 58, no. 3-4, pp. 379–397, 2010.
- M. B. Dhakne and K. D. Kucche, “Existence of a mild solution of mixed Volterra-Fredholm functional integrodifferential equation with nonlocal condition,” Applied Mathematical Sciences, vol. 5, no. 5–8, pp. 359–366, 2011.
- N. Abada, M. Benchohra, and H. Hammouche, “Existence results for semilinear differential evolution equations with impulses and delay,” CUBO. A Mathematical Journal, vol. 12, no. 2, pp. 1–17, 2010.
- X. Xu, “Existence for delay integrodifferential equations of Sobolev type with nonlocal conditions,” International Journal of Nonlinear Science, vol. 12, no. 3, pp. 263–269, 2011.
- Y. Yang and J. Wang, “On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces,” Opuscula Mathematica, vol. 31, no. 3, pp. 443–455, 2011.
- Q. Liu and R. Yuan, “Existence of mild solutions for semilinear evolution equations with non-local initial conditions,” Nonlinear Analysis, vol. 71, no. 9, pp. 4177–4184, 2009.
- A. Boucherif and R. Precup, “Semilinear evolution equations with nonlocal initial conditions,” Dynamic Systems and Applications, vol. 16, no. 3, pp. 507–516, 2007.
- D. N. Chalishajar, “Controllability of mixed Volterra-Fredholm-type integro-differential systems in Banach space,” Journal of the Franklin Institute, vol. 344, no. 1, pp. 12–21, 2007.
- J. H. Liu and K. Ezzinbi, “Non-autonomous integrodifferential equations with non-local conditions,” Journal of Integral Equations and Applications, vol. 15, no. 1, pp. 79–93, 2003.
- K. Balachandran and R. Sakthivel, “Controllability of semilinear functional integrodifferential systems in Banach spaces,” Kybernetika, vol. 36, no. 4, pp. 465–476, 2000.
- Y. P. Lin and J. H. Liu, “Semilinear integrodifferential equations with nonlocal Cauchy problem,” Nonlinear Analysis, vol. 26, no. 5, pp. 1023–1033, 1996.
- K. Malar, “Existence of mild solutions for nonlocal integro-di erential equations with measure of noncompactness,” Internationnal Journal of Mathematics and Scientic Computing, vol. 1, pp. 86–91, 2011.
- H.-B. Shi, W.-T. Li, and H.-R. Sun, “Existence of mild solutions for abstract mixed type semilinear evolution equations,” Turkish Journal of Mathematics, vol. 35, no. 3, pp. 457–472, 2011.
- T. Zhu, C. Song, and G. Li, “Existence of mild solutions for abstract semilinear evolution equations in Banach spaces,” Nonlinear Analysis, vol. 75, no. 1, pp. 177–181, 2012.
- Z. Fan, Q. Dong, and G. Li, “Semilinear differential equations with nonlocal conditions in Banach spaces,” International Journal of Nonlinear Science, vol. 2, no. 3, pp. 131–139, 2006.
- X. Xue, “Existence of solutions for semilinear nonlocal Cauchy problems in Banach spaces,” Electronic Journal of Differential Equations, vol. 64, pp. 1–7, 2005.
- S. K. Ntouyas and P. Ch. Tsamatos, “Global existence for semilinear evolution equations with nonlocal conditions,” Journal of Mathematical Analysis and Applications, vol. 210, no. 2, pp. 679–687, 1997.
- L. Byszewski and H. Akca, “Existence of solutions of a semilinear functional-differential evolution nonlocal problem,” Nonlinear Analysis, vol. 34, no. 1, pp. 65–72, 1998.
- H.-P. Heinz, “On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions,” Nonlinear Analysis, vol. 7, no. 12, pp. 1351–1371, 1983.
- D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear Integral Equations in Abstract Spaces, vol. 373 of Mathematics and Its Applications, Kluwer Academic, Dordrecht, The Netherlands, 1996.
- H. Mönch, “Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces,” Nonlinear Analysis, vol. 4, no. 5, pp. 985–999, 1980.
- R. Ye, Q. Dong, and G. Li, “Existence of solutions for double perturbed neutral functional evolution equation,” International Journal of Nonlinear Science, vol. 8, no. 3, pp. 360–367, 2009.
- A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, NY, USA, 1969.