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Journal of Function Spaces
Volume 2018, Article ID 9269458, 7 pages
https://doi.org/10.1155/2018/9269458
Research Article

Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications

Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050, China

Correspondence should be addressed to Wenguo Shen; moc.361@963gwnehs

Received 8 August 2017; Accepted 20 November 2017; Published 9 January 2018

Academic Editor: Vijay Gupta

Copyright © 2018 Wenguo Shen. 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 shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: , in , , on , where is the Hessian matrix of , where is the unit open ball of , is a radially symmetric weighted function and on any subinterval of , is a positive parameter, and the nonlinear term , but is not necessarily differentiable at the origin and infinity with respect to , where . Some applications are given to the Monge-Ampère equations and we use global bifurcation techniques to prove our main results.