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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 1024950, 3 pages
https://doi.org/10.1155/2017/1024950
Letter to the Editor

Comment on “Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications”

1Baku State University, AZ1148 Baku, Azerbaijan
2Institute of Mathematics and Mechanics NAS of Azerbaijan, AZ1141 Baku, Azerbaijan

Correspondence should be addressed to Ziyatkhan Aliyev

Received 23 March 2016; Accepted 8 December 2016; Published 5 April 2017

Academic Editor: Juan R. Torregrosa

Copyright © 2017 Ziyatkhan Aliyev. 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

In the recent paper W. Shen and T. He and G. Dai and X. Han established unilateral global bifurcation result for a class of nonlinear fourth-order eigenvalue problems. They show the existence of two families of unbounded continua of nontrivial solutions of these problems bifurcating from the points and intervals of the line trivial solutions, corresponding to the positive or negative eigenvalues of the linear problem. As applications of this result, these authors study the existence of nodal solutions for a class of nonlinear fourth-order eigenvalue problems with sign-changing weight. Moreover, they also establish the Sturm type comparison theorem for fourth-order problems with sign-changing weight. In the present comment, we show that these papers of above authors contain serious errors and, therefore, unfortunately, the results of these works are not true. Note also that the authors used the results of the recent work by G. Dai which also contain gaps.