Nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type

Journal of Mathematical Analysis and Applications

Volumn 325, Issue 2, 2007, Pages 830-842

  Chen, Lijing ^a   Sun, Jitao ^a  

^a TONGJI UNIVERSITY   (China)

Author keywords

Extremal solutions; Impulsive differential equations; Monotone iterative technique; Nonlinear boundary; Upper and lower solution

Indexed keywords

EID: 33750331083     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.01.084     Document Type: Article

References (24)

1. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
2. Samoilenko A.M., and Perestyuk N.A. Impulsive Differential Equations (1995), World Scientific, Singapore
3. Rogovchenko Y.V. Impulsive evolution systems: Main results and new trends. Dyn. Contin. Discrete Impuls. Syst. 3 (1997) 57-88
4. Sun J.T. Stability criteria of impulsive differential system. Appl. Math. Comput. 156 (2004) 85-91
5. Sun J.T., Zhang Y.P., and Wu Q.D. Less conservative conditions for asymptotic stability of impulsive control systems. IEEE Trans. Automat. Control 48 5 (2003) 829-831
6. Nieto J.J., and Rodríguez-López R. Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions. Comput. Math. Appl. 40 (2000) 433-442
7. Nieto J.J. Differential inequalities of functional perturbations of first-order ordinary differential equations. Appl. Math. Lett. 15 (2002) 173-179
8. L.J. Chen, J.T. Sun, Nonlinear boundary problem of first order impulsive functional differential equations, J. Math. Anal. Appl., in press
9. T. Jankowski, Boundary value problems for first order differential equations of mixed type, Nonlinear Anal., in press
10. Jiang D.Q., Nieto J.J., and Zuo W.J. On monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations. J. Math. Anal. Appl. 289 (2004) 691-699
11. Jankowski T. Existence of solutions of boundary value problems for differential equations with delayed argument. J. Comput. Appl. Math. 156 (2003) 239-252
12. Jankowski T. Advanced differential equations with nonlinear boundary conditions. J. Math. Anal. Appl. 304 (2005) 490-503
13. Yebdri M., Bouguima S.M., and Arino O. An iterative method for functional differential equations. Appl. Math. Comput. 161 (2005) 265-269
14. Song G.X., and Zhu X.L. Extremal solutions of periodic boundary value problems for first order integro-differential equations of mixed type. J. Math. Anal. Appl. 300 (2004) 1-11
15. Nieto J.J., and Rodríguez-López R. Remarks on periodic boundary value problems for functional differential equations. J. Comput. Appl. Math. 158 (2003) 339-353
16. Ding W., Mi J.R., and Han M.A. Periodic boundary value problem for the first order impulsive functional differential equations. Appl. Math. Comput. 165 (2005) 433-446
17. He Z.M., and He X.M. Monotone iterative technique for impulsive integro-differential equations with periodic boundary condition. Comput. Math. Appl. 48 (2004) 73-84
18. L.J. Chen, J.T. Sun, Boundary value problem of second order impulsive functional differential equations, J. Math. Anal. Appl., in press
19. He X., Ge W., and He Z. First-order impulsive functional differential equations with periodic boundary value conditions. Indian J. Pure Appl. Math. 33 (2002) 1257-1273
20. Zhang F., Ma Z., and Yan J. Periodic boundary value problems and monotone iterative methods for first-order impulsive differential equations with delay. Indian J. Pure Appl. Math. 32 (2001) 1695-1707
21. He Z.M., and Yu J.S. Periodic boundary value problem for first-order impulsive functional differential equations. J. Comput. Appl. Math. 138 (2002) 205-217
22. J.J. Nieto, R. Rodríguez-López, Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations, J. Math. Anal. Appl., in press
23. Franco D., Liz E., Nieto J.J., and Rogovchenko Y. A contribution to the study of functional differential equations with impulses. Math. Nachr. 218 (2000) 49-60
24. Nieto J.J. Periodic boundary value problems for first order impulsive ordinary differential equations. Nonlinear Anal. 51 (2002) 1223-1232