Nonlinear impulsive integro-differential equations of mixed type with time-varying generating operators and optimal controls

Dynamic Systems and Applications

Volumn 16, Issue 3, 2007, Pages 481-496

  Peng, Y ^a   Xiang, X ^a   Wei, W ^a  

^a GUIZHOU UNIVERSITY   (China)

Author keywords

Compactness; Existence; Fractional power space; Integral operator of mixed type; Optimal control; PC mind solution; Semigroup

Indexed keywords

EID: 56649099332     PISSN: 10562176     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. N. U. Ahmed, Optimal impulse control for impulsive Systems in Banach spaces, Int. J. Differential Equations Appl., 1 (2000), no.1, 37-52.
2. N. U. Ahmed, K. L. Teo and S. H. Hou, Nonlinear impulsive-systems on infinite dimensional spaces, Nonlinear Analysis, 54 (2003), 907-925.
3. H. Amann, Periodic solutions of semilinear parabolic equations, Nonlinear Analysis: A collection of papers in Honour of Erich Rothe, Academic Press, New York, 1978, 1-29.
4. K. Balachandran and M. Chandrasekaran, Nonlocal Cauchy problem for quasilinear integro-differential equation in Banach spaces, Dynam. Systems Appl. 8 (1999), no.1, 35-43.
5. Chen Yan-lai, Solutions of a boundary value problem for a class of nonlinear integro- differential equations in Banach spaces, Acta Analysis Punctionalis Applicata, 5(2003), no.4, 322-329.
6. Fei Guo, Lishan Liu, Yonghong Wu and Peg-Foo Siew, Global solutions of initial value problems for nonlinear second-order impulsive integro-differential equations of mixed type in Banach spaces, Nonlinear Analysis, 61(2005), 1363-1382.
7. Zhimin He and Xiaoming He, Periodic boundary value problems for first order impulsive integro-differential equations of mixed type, J. Mathematical Analysis and Applications, 296(2004), 8-20.
8. S. Hu and N. S. Papageorgiou, Handbook of multivalued Analysis (Theory), Kluwer Academic Publishers, Dordrecht Boston, London, 1997.
9. V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of impulsive differential equations, World Scientific, Singapore-London, 1989.
10. L. S. Liu, C. X. Wu and F. Guo, A unique solution of initial value problems for first-order impulsive integro-differential equations of mixed type in Banach space, J. Mathematical Analysis and Applications, 275(2002), 369-385.
11. A. Pazy, Semigroup of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983.
12. Peng Yunfei, Chen Xiaoyuan and Wei Wei, Existence of a-mild solutions for a class of nonlinear evolution equations, Guizhou Science, 20(2002), no.3, 30-36.
13. W. Wei, X. Xiang and Y. Peng, Nonlinear impulsive integro-differential equation of mixed type and optimal controls, Optimization, 55(2006), no.1-2,141-156.
14. X. Xiang and Jiang Yang, Optimal control of systems governed by a class of integro-differential equations, J. Guizhou University, 4(2003), no.4, 335-342.
15. Xiang Xiaoling and Kuang Huawu, Delay systems and optimal controls, Acta Mathematices Applicates Sinica, 16(2000), no.1, 27-35.
16. X. Xiang, Y. Peng and W. Wei, A general class of nonlinear impulsive integro-differential equations and optimal controls on Banach spaces, Discrete and Continuous Dynamical Systems, Supplement Volume2005, 911-919.