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Open Access Open Badges Research Article

Solvability of Second-Order -Point Boundary Value Problems with Impulses

Jianli Li1* and Sanhui Liu12

Author Affiliations

1 Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China

2 Department of Mathematics, Zhuzhou Professional Technology College, Zhuzhou, Hunan 412000, China

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Boundary Value Problems 2007, 2007:097067  doi:10.1155/2007/97067

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/097067

Received:1 April 2007
Accepted:30 August 2007
Published:22 November 2007

© 2007 Li and Liu

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

By Leray-Schauder continuation theorem and the nonlinear alternative of Leray-Schauder type, the existence of a solution for an -point boundary value problem with impulses is proved.


  1. Gupta, CP: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation. Journal of Mathematical Analysis and Applications. 168(2), 540–551 (1992). Publisher Full Text OpenURL

  2. Gupta, CP, Ntouyas, SK, Tsamatos, PCh: Solvability of an -point boundary value problem for second order ordinary differential equations. Journal of Mathematical Analysis and Applications. 189(2), 575–584 (1995). Publisher Full Text OpenURL

  3. Ma, R: Existence of positive solutions for superlinear semipositone -point boundary-value problems. Proceedings of the Edinburgh Mathematical Society. Series II. 46(2), 279–292 (2003). Publisher Full Text OpenURL

  4. Agarwal, RP, O'Regan, D: A multiplicity result for second order impulsive differential equations via the Leggett Williams fixed point theorem. Applied Mathematics and Computation. 161(2), 433–439 (2005). Publisher Full Text OpenURL

  5. Mawhin, J: Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Regional Conference Series in Mathematics,p. v+122. American Mathematical Society, Providence, RI, USA (1979)

  6. Agarwal, RP, O'Regan, D, Wong, PJY: Positive Solutions of Differential, Difference and Integral Equations,p. xii+417. Kluwer Academic, Dordrecht, The Netherlands (1999)

  7. Baĭnov, DD, Simeonov, PS: Impulsive Differential Equations: Periodic Solutions and Applications, Pitman Monographs and Surveys in Pure and Applied Mathematics,p. x+228. Longman Scientific & Technical, Harlow, UK (1993)