Comment on “Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications”
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-3, 3 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-04-05
Country of Publication
Egypt
No. of Pages
3
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Aliyev, Ziyatkhan S.. 2017. Comment on “Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications”. Discrete Dynamics in Nature and Society،Vol. 2017, no. 2017, pp.1-3.
https://search.emarefa.net/detail/BIM-1151103
Modern Language Association (MLA)
Aliyev, Ziyatkhan S.. Comment on “Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications”. Discrete Dynamics in Nature and Society No. 2017 (2017), pp.1-3.
https://search.emarefa.net/detail/BIM-1151103
American Medical Association (AMA)
Aliyev, Ziyatkhan S.. Comment on “Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications”. Discrete Dynamics in Nature and Society. 2017. Vol. 2017, no. 2017, pp.1-3.
https://search.emarefa.net/detail/BIM-1151103
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151103