Guoqing Zhang, Xiping Liu, Sanyang Liu
Abstract:
We study the Nehari manifold for a class of quasilinear elliptic
systems involving a pair of (p,q)-Laplacian operators
and a parameter. We prove the existence of a nonnegative
nonsemitrivial solution for the systems by discussing properties
of the Nehari manifold, and so global bifurcation results are
obtained. Thanks to Picone's identity, we also prove a
nonexistence result.
Submitted July 16, 2004. Published February 8, 2005.
Math Subject Classifications: 35B32, 35J20,35J50, 35P15.
Key Words: Nehari manifold; (p,q)-Laplacian; variational methods.
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Guoqing Zhang Department of Applied Mathematics, Xidian University Xi'an Shaanxi, 710071, China College of Science University of Shanghai for science and Technology Shanghai, 200093, China email: zgqw2001@sina.com.cn |
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Xiping Liu College of Science University of Shanghai for science and Technology Shanghai, 200093, China email: xipingliu@163.com |
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Sanyang Liu Department of Applied Mathematics Xidian University Xi'an Shaanxi, 710071, China email: liusanyang@263.net |
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