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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 783509, 9 pages
Research Article

Upper and Lower Solutions for -Point Impulsive BVP with One-Dimensional -Laplacian

1School of Science, China University of Geosciences, Beijing 100083, China
2College of Science, Hebei University of Engineering, Handan 056038, China
3Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 30 July 2013; Revised 13 October 2013; Accepted 15 October 2013

Academic Editor: Gabriele Bonanno

Copyright © 2013 Junfang Zhao et al. 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.


Upper and lower solutions theories are established for a kind of -point impulsive boundary value problems with -Laplacian. By using such techniques and the Schauder fixed point theorem, the existence of solutions and positive solutions is obtained. Nagumo conditions play an important role in the nonlinear term involved with the first-order derivatives.