Multiple positive solutions of multi-point boundary value problem for second-order impulsive differential equations

Journal of Computational and Applied Mathematics

Volumn 223, Issue 1, 2009, Pages 438-448

  Meiqiang, Feng ^a   Dongxiu, Xie ^a  

^a BEIJING INFORMATION SCIENCE AND TECHNOLOGY UNIVERSITY   (China)

Author keywords

Completely continuous; Existence; Fixed point theory; Multi point boundary value problem with impulse effects; Positive solution

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEMS; SOLUTIONS; TURBULENT FLOW;

COMPLETELY CONTINUOUS; EXISTENCE; FIXED-POINT THEORY; MULTI-POINT BOUNDARY VALUE PROBLEM WITH IMPULSE EFFECTS; POSITIVE SOLUTION;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 54249146999     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.01.024     Document Type: Article

References (31)

1. Lakshmikantham V., Bainov D., and Simeonov P. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
2. Bainov D., and Simeonov P. Systems with Impulse Effect (1989), Ellis Horwood, Chichister
3. Samoilenko A.M., and Perestyuk N.A. Impulsive Differential Equations (1995), World Scientific, Singapore
4. Feng M., and Pang H. A class of three point boundary value problems for second order impulsive integro-differential equations in Banach spaces. Nonlinear Anal. (2007) 10.1016/j.na.2007.11.033
5. Wei Z. Periodic boundary value problems for second order impulsive integrodifferential equations of mixed type in Banach spaces. J. Math. Anal. Appl. 195 (1995) 214-229
6. Hristova S., and Bainov D. Monotone-iterative techniques of V. Lakshmikantham for a boundary value problem for systems of impulsive differential-difference equations. J. Math. Anal. Appl. 1997 (1996) 1-13
7. Liu X., and Guo D. Periodic boundary value problems for a class of second-order impulsive integro-differential equations in Banach spaces. Appl. Math. Comput. 216 (1997) 284-302
8. Agarwal R.P., and O'Regan D. Multiple nonnegative solutions for second order impulsive differential equations. Appl. Math. Comput. 114 (2000) 51-59
9. Liu B., and Yu J. Existence of solution for m-point boundary value problems of second-order differential systems with impulses. Appl. Math. Comput. 125 (2002) 155-175
10. Ding W., and Han M. Periodic boundary value problem for the second order impulsive functional differential equations. Appl. Math. Comput. 155A (2004) 709-726
11. Lee E., and Lee Y. Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equation. Appl. Math. Comput. 158 (2004) 745-759
12. Il'in V., and Moiseev E. Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator. Differ. Equ. 23 (1987) 979-987
13. Ma R. Multiplicity of positive solutions for second-order three-point boundary value problems. Comput. Math. Appl. 40 (2000) 193-204
14. Ma R., and Castaneda N. Existence of solutions of nonlinear m-point boundary-value problems. J. Math. Anal. Appl. 256 (2001) 556-567
15. Ma R., and Wang H. Positive solutions of nonlinear three-point boundary-value problems. J. Math. Anal. Appl. 279 (2003) 216-227
16. Ma R., and Thompson B. Positive solutions for nonlinear m-point eigenvalue problems. J. Math. Anal. Appl. 297 (2004) 24-37
17. Ma R. Multiple positive solutions for nonlinear m-point boundary value problems. Appl. Math. Comput. 148 (2004) 249-262
18. Guo D., and Lakshmikantham V. Nonlinear Problems in Abstract Cones (1988), Academic Press, Inc., NewYork
19. Bai Z., and Du Z. Positive solutions for some second-order four-point boundary value problems. J. Math. Anal. Appl. 330 (2007) 34-50
20. Bai Z., Ge W., and Wang Y. Multiplicity results for some second-order four-point boundary value problems. Nonlinear Anal. 60 (2005) 491-500
21. Bai Z., Li W., and Ge W. Existence and multiplicity of solutions for four-point boundary value problems at resonance. Nonlinear Anal. 60 (2005) 1151-1162
22. He X., and Ge W. Triple positive solutions for second-order three-point boundary value problems. J. Math. Anal. Appl. 268 (2002) 256-265
23. Guo Y., and Ge W. Positive solutions for three-point boundary value problems with dependence on the first order derivative. J. Math. Anal. Appl. 290 (2004) 291-301
24. Cheung W., and Ren J. Positive solutions for m-point boundary-value problems. J. Math. Anal. Appl. 303 (2005) 565-575
25. Gupta C. A generalized multi-point boundary value problem for second order ordinary differential equations. Appl. Math. Comput. 89 (1998) 133-146
26. Feng W. On a m-point nonlinear boundary value problems. Nonlinear Anal. 30 (1997) 5369-5370
27. Feng W., and Webb J.R.L. Solvability of a m-point boundary value problems with nonlinear growth. J. Math. Anal. Appl. 212 (1997) 467-480
28. Feng W., and Webb J.R.L. Solvability of a three-point nonlinear boundary value problems at resonance. Nonlinear Anal. 30 (1997) 3227-3238
29. Zhang Z., and Wang J. The upper and lower solution method for a class of singular nonlinear second order three-point boundary value problems. J. Comput. Appl. Math. 147 (2002) 41-52
30. Zhang G., and Sun J. Positive solutions of m-point boundary value problems. J. Math. Anal. Appl. 291 (2004) 406-418
31. Feng M., and Ge W. Positive solutions for a class of m-point singular boundary value problems. Math. Comput. Modelling 46 (2007) 375-383