Open Access

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

Boundary Value Problems20072007:097067

DOI: 10.1155/2007/97067

Received: 1 April 2007

Accepted: 30 August 2007

Published: 22 November 2007


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.


Authors’ Affiliations

Department of Mathematics, Hunan Normal University
Department of Mathematics, Zhuzhou Professional Technology College


  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 1992,168(2):540-551. 10.1016/0022-247X(92)90179-HMATHMathSciNetView ArticleGoogle Scholar
  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 1995,189(2):575-584. 10.1006/jmaa.1995.1036MATHMathSciNetView ArticleGoogle Scholar
  3. Ma R:Existence of positive solutions for superlinear semipositone -point boundary-value problems. Proceedings of the Edinburgh Mathematical Society. Series II 2003,46(2):279-292. 10.1017/S0013091502000391MATHMathSciNetView ArticleGoogle Scholar
  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 2005,161(2):433-439. 10.1016/j.amc.2003.12.096MATHMathSciNetView ArticleGoogle Scholar
  5. Mawhin J: Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Regional Conference Series in Mathematics. Volume 40. American Mathematical Society, Providence, RI, USA; 1979:v+122.Google Scholar
  6. Agarwal RP, O'Regan D, Wong PJY: Positive Solutions of Differential, Difference and Integral Equations. Kluwer Academic, Dordrecht, The Netherlands; 1999:xii+417.MATHView ArticleGoogle Scholar
  7. Baĭnov DD, Simeonov PS: Impulsive Differential Equations: Periodic Solutions and Applications, Pitman Monographs and Surveys in Pure and Applied Mathematics. Volume 66. Longman Scientific & Technical, Harlow, UK; 1993:x+228.Google Scholar


© J. Li and S. Liu. 2007

This article is published under license to BioMed Central Ltd. 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.