Periodic boundary value problems of second-order impulsive differential equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 70, Issue 1, 2009, Pages 262-273

  Yao, Meiping ^a   Zhao, Aimin ^a   Yan, Jurang ^a  

^a SHANXI UNIVERSITY   (China)

Author keywords

Boundary value problem; Impulsive differential equation; Monotone iterative technique; Second order; Upper and lower solutions

Indexed keywords

BOUNDARY VALUE PROBLEMS; INITIAL VALUE PROBLEMS; ITERATIVE METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

BOUNDARY VALUE PROBLEM; IMPULSIVE DIFFERENTIAL EQUATION; MONOTONE ITERATIVE TECHNIQUE; SECOND ORDER; UPPER AND LOWER SOLUTIONS;

DIFFERENTIAL EQUATIONS;

EID: 55549087578     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.11.050     Document Type: Article

References (25)

1. Agarwal R.P., and O'Regan D. Infinite Interval Problems for Differential, Difference and Integral Equations (2001), Kluwer, Dordrecht
2. Cabada A. The method of lower and upper solutions for second, third, fourth and higher order boundary value problems. J. Math. Anal. Appl. 185 (1994) 302-320
3. Cabada A., and Nieto J.J. A generalization of the monotone iterative technique for nonlinear second order periodic boundary value problems. J. Math. Anal. Appl. 151 (1990) 181-189
4. Cabada A., and Nieto J.J. Extremal solutions of second order nonlinear periodic boundary value problems. Appl. Math. Comput. 40 (1990) 135-145
5. Chen L., and Sun J. Nonlinear boundary value problem of first order impulsive functional differential equations. J. Math. Anal. Appl. 318 (2006) 726-741
6. Chen L., and Sun J. Boundary value problem of second order impulsive functional differential equations. J. Math. Anal. Appl. 323 (2006) 708-720
7. Chen L., and Sun J. Nonlinear boundary problem of first order impulsive integro-differential equations. J. Comput. Appl. Math. 202 (2007) 392-401
8. Ding W., and Han M. Periodic boundary value problem for the second order impulsive functional differential equations. Appl. Math. Comput. 155 (2004) 709-726
9. Ding W., Han M., and Mi J. Periodic boundary value problem for the second-order impulsive functional differential equations. Comput. Math. Appl. 50 (2005) 491-507
10. Gao W.J., and Wang J.Y. On a nonlinear second order periodic boundary value problem with Caratheodory functions. Ann. Polon. Math. 62 (1995) 283-291
11. He Z., and Yu J. Periodic boundary value problem for first-order impulsive ordinary differential equations. J. Math. Anal. Appl. 272 (2002) 67-78
12. Jankowski T. Existence of solutions of boundary value problems for differential equations with delayed arguments. J. Comput. Appl. Math. 156 (2003) 239-252
13. Jankowski T. Monotone method for second-order delayed differential equations with boundary value conditions. Appl. Math. Comput. 149 (2004) 589-598
14. Jankowski T. Existence of solutions for second order impulsive differential equations with deviating arguments. Nonlinear Anal. 67 (2007) 1764-1774
15. Jiang D., Nieto J.J., and Zuo W. 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
16. Jiang D., and Wei J. Monotone method for first- and second-order periodic boundary value problems and periodic solutions of functional differential equations. Nonlinear Anal. 50 (2002) 885-898
17. Jiang D., Fan M., and Wan A. A monotone method for constructing extremal solutions to second-order periodic boundary value problems. J. Comput. Appl. Math. 136 (2001) 189-197
18. Khan R.A., and Rafique M. Existence and multiplicity results for some three-point boundary value problems. Nonlinear Anal. 66 (2007) 1686-1697
19. Ladde G.S., Lakshmikantham V., and Vatsala A.S. Monotone Iterative Techniques for Nonlinear Differential Equations (1985), Pitman, Boston
20. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
21. Nieto J.J. Nonlinear second order periodic boundary problems with Caratheodory functions. Appl. Anal. 34 (1989) 111-128
22. Rachunková I., and Tvrdý M. Existence results for impulsive second-order periodic problems. Nonlinear Anal. 59 (2004) 133-146
23. Samoilenko A.M., and Perestyuk N.A. Impulsive Differential Equations (1995), World Scientific, Singapore
24. Wang M.X., Cabada A., and Nieto J.J. Monotone method for nonlinear second-order periodic boundary value problems with Caratheodory functions. Ann. Polon. Math. 58 (1993) 221-235
25. Yang X., and Shen J. Periodic boundary value problems for second-order impulsive integro-differential equations. J. Comput. Appl. Math. (2006) 10.1016/j.cam.2006.10.082