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Open Access Open Badges Research Article

Existence and Numerical Method for Nonlinear Third-Order Boundary Value Problem in the Reproducing Kernel Space

Xueqin Lü12* and Minggen Cui1

Author Affiliations

1 Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China

2 School of Mathematics and Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, China

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Boundary Value Problems 2010, 2010:459754  doi:10.1155/2010/459754

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2010/1/459754

Received:14 July 2009
Revisions received:12 November 2009
Accepted:11 January 2010
Published:2 February 2010

© 2010 The Author(s).

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.


We are concerned with general third-order nonlinear boundary value problems. An existence theorem of solution is given under weaker conditions. In the meantime, an iterative algorithm with global convergence is presented. The higher order derivatives of approximate solution is obtained by using this method can approximate the corresponding derivatives of exact solution well.

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