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Journal of Function Spaces
Volume 2016, Article ID 3495170, 6 pages
Research Article

Liouville Theorem for Some Elliptic Equations with Weights and Finite Morse Indices

1Electronic Information School, Wuhan University, Hubei 430071, China
2Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Hubei 430071, China
3Université de Versailles Saint-Quentin, Laboratoire Données et Algorithmes pour une Ville Intelligente et Durable (DAVID), 78035 Versailles, France

Received 11 December 2015; Revised 20 April 2016; Accepted 21 April 2016

Academic Editor: Simone Secchi

Copyright © 2016 Qiongli Wu et al. 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.


We establish the nonexistence of solution for the following nonlinear elliptic problem with weights: in , where is a positive parameter. Suppose that , for or , for ; we will show that this equation does not possess nontrivial bounded solution with finite Morse index.