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International Journal of Differential Equations
Volume 2010 (2010), Article ID 673526, 12 pages
http://dx.doi.org/10.1155/2010/673526
Research Article

Multiple Solutions of Quasilinear Elliptic Equations in 𝑁

Department of Natural Sciences, Center for General Education, Chang Gung University, Taoyuan 333, Taiwan

Received 1 October 2009; Revised 15 January 2010; Accepted 1 March 2010

Academic Editor: Martin D. Schechter

Copyright © 2010 Huei-li Lin. 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

Assume that 𝑄 is a positive continuous function in 𝑁 and satisfies some suitable conditions. We prove that the quasilinear elliptic equation Δ 𝑝 𝑢 + | 𝑢 | 𝑝 2 𝑢 = 𝑄 ( 𝑧 ) | 𝑢 | 𝑞 2 𝑢 in 𝑁 admits at least two solutions in 𝑁 (one is a positive ground-state solution and the other is a sign-changing solution).