Initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 64, Issue 11, 2006, Pages 2562-2574

  Zhang, Xinguang ^a   Liu, Lishan ^a  

^a QUFU NORMAL UNIVERSITY   (China)

Author keywords

Banach fixed point theorem; Initial value problem; Nonlinear second order impulsive equation

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

BANACH SPACES; FIXED POINT THEOREM; NONLINEAR SECOND ORDER IMPULSIVE EQUATION;

INITIAL VALUE PROBLEMS;

EID: 33644957636     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.09.004     Document Type: Article

References (13)

1. G.Q. Chai Initial value problems for nonlinear second order impulsive integro-differential equations in Banach space Acta Math. Sinica 20 3 2000 351 359 (in Chinese)
2. K. Deimling Nonlinear Functional Analysis 1985 Springer Berlin
3. D.J. Guo Solutions of nonlinear integro-differential equations of mixed type in Banach spaces J. Appl. Math. Simulation 12 1989 1 11
4. D.J. Guo Initial value problems for nonlinear second-order impulsive integro-differential equations in Banach spaces J. Math. Anal. Appl. 200 1996 1 13
5. D.J. Guo, and V. Lakshmikantham Nonlinear Problems in Abstract Cones 1988 Academic Press, Inc. New York
6. D.J. Guo, V. Lakshmikantham, and X.Z. Liu Nonlinear Integral Equations in Abstract Spaces 1996 Kluwer Academic Publishers Dordrecht
7. V. Lakshmikantham Some problems in integro-differential equations of Volterra type J. Integral Equations, Suppl. 10 1985 137 146
8. V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov Theory of Impulsive Differential Equations 1989 World Scientific Singapore
9. V. Lakshmikantham, and S. Leela Nonlinear Differential Equations in Abstract Space 1981 Pergamon Press New York
10. L.S. Liu Iterative method for solutions and coupled quasi-solutions of nonlinear Fredholm integral equations in ordered Banach spaces Indian J. Pure Appl. Math. 27 1996 959 972
11. 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 Spaces J. Math. Anal. Appl. 275 2002 369 385
12. L.S. Liu, C.X. Wu, and F. Guo Existence theorems of global solutions of initial value problem for nonlinear integro-differential equations of mixed type in Banach spaces and applications Comput. Math. Appl. 47 2004 13 22
13. J.L. Sun, and Y.H. Ma Initial value problems for the second order mixed monotone type of impulsive differential equations in Banach Spaces J. Math. Anal. Appl. 247 2000 506 516