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Abstract and Applied Analysis
Volume 2014, Article ID 947139, 11 pages
Research Article

Multiplicity of Solutions to a Potential Operator Equation and Its Applications

1College of Sciences, Hohai University, Nanjing 210098, China
2Department of Mathematics and Physics, Hohai University, Changzhou Campus, Changzhou 213022, China

Received 12 July 2014; Accepted 27 August 2014; Published 22 October 2014

Academic Editor: M. Victoria Otero-Espinar

Copyright © 2014 Jincheng Huang. 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 consider the multiplicity of solutions for operator equation involving homogeneous potential operators. With the help of Nehari manifold and fibering maps, we prove that such equation has at least two nontrivial solutions. Furthermore, we apply this result to prove the existence of two nonnegative solutions for three types of quasilinear elliptic systems involving (p, q)-Laplacian operator and concave-convex nonlinearities.