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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 590968, 9 pages
Research Article

Spectrum of Discrete Second-Order Difference Operator with Sign-Changing Weight and Its Applications

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 13 March 2014; Accepted 28 March 2014; Published 13 April 2014

Academic Editor: Mustafa Kulenović

Copyright © 2014 Ruyun Ma 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.


Let be an integer, and let. We discuss the spectrum of discrete linear second-order eigenvalue problems ,  , where is a parameter, changes sign and on . At last, as an application of this spectrum result, we show the existence of sign-changing solutions of discrete nonlinear second-order problems by using bifurcate technique.