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Journal of Function Spaces
Volume 2018 (2018), Article ID 9857038, 7 pages
https://doi.org/10.1155/2018/9857038
Research Article

On Fourth-Order Elliptic Equations of Kirchhoff Type with Dependence on the Gradient and the Laplacian

1College of Science, Hohai University, Nanjing 210098, China
2College of Science, China Pharmaceutical University, Nanjing 211198, China
3School of Mechanical Engineering, Guizhou Institute of Technology, Guiyang 550003, China

Correspondence should be addressed to Yunhai Wang; moc.621@aaunhygnaw

Received 26 September 2017; Accepted 20 November 2017; Published 2 January 2018

Academic Editor: Dhananjay Gopal

Copyright © 2018 Yuanfang Ru 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.

Abstract

We consider a nonlocal fourth-order elliptic equation of Kirchhoff type with dependence on the gradient and Laplacian , in , , , on , where , are positive constants. We will show that there exists such that the problem has a nontrivial solution for through an iterative method based on the mountain pass lemma and truncation method developed by De Figueiredo et al., 2004.