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Journal of Applied Mathematics
Volume 2014, Article ID 810193, 9 pages
http://dx.doi.org/10.1155/2014/810193
Research Article

Existence of Sign-Changing Solutions to Equations Involving the One-Dimensional -Laplacian

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

Received 23 March 2014; Accepted 21 July 2014; Published 17 August 2014

Academic Editor: Mehmet Sezer

Copyright © 2014 Ruyun Ma and Lingfang Jiang. 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

We consider the equations involving the one-dimensional -Laplacian   , and where and . We show the existence of sign-changing solutions under the assumptions and . We also show that has exactly one solution having specified nodal properties for for some . Our main results are based on quadrature method.