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Abstract and Applied Analysis
Volume 2012, Article ID 658010, 16 pages
Research Article

Solvability of Three-Point Boundary Value Problems at Resonance with a -Laplacian on Finite and Infinite Intervals

1School of Sciences, China University of Geosciences, Beijing 100083, China
2School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
3Department of Foundation, North China Institute of Science and Technology, Beijing 101601, China

Received 1 September 2012; Accepted 9 October 2012

Academic Editor: Yonghui Xia

Copyright © 2012 Hairong Lian 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.


Three-point boundary value problems of second-order differential equation with a p-Laplacian on finite and infinite intervals are investigated in this paper. By using a new continuation theorem, sufficient conditions are given, under the resonance conditions, to guarantee the existence of solutions to such boundary value problems with the nonlinear term involving in the first-order derivative explicitly.