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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 798796, 17 pages
http://dx.doi.org/10.1155/2012/798796
Research Article

Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales

1School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China
2Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 25 December 2011; Accepted 27 March 2012

Academic Editor: Yonghong Wu

Copyright © 2012 Hua Luo and Chenghua Gao. 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.

Abstract

Let be a time scale and , . We study the nonlinear fourth-order eigenvalue problem on , , , and obtain the existence and nonexistence of positive solutions when and , respectively, for some . The main tools to prove the existence results are the Schauder fixed point theorem and the upper and lower solution method.