Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T17:22:04.501Z Has data issue: false hasContentIssue false
  • English
  • Français

Positive periodic solutions for singular fourth-order differential equations with a deviating argument

Part of: Boundary value problems Functional-differential and differential-difference equations

Published online by Cambridge University Press:  10 May 2018

Fanchao Kong  and
Zaitao Liang
Fanchao Kong
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, People's Republic of China (fanchaokong88@sohu.com)
Zaitao Liang
Affiliation:
Department of Mathematics, College of Science, Hohai University, Nanjing 210098, People's Republic of China
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we study the singular fourth-order differential equation with a deviating argument:

By using Mawhin's continuation theorem and some analytic techniques, we establish some criteria to guarantee the existence of positive periodic solutions. The significance of this paper is that g has a strong singularity at x = 0 and satisfies a small force condition at x = ∞, which is different from the known ones in the literature.

Keywords

positive periodic solutionsfourth-order differential equationsMawhin's continuation theoremdeviating argumentsingularity

MSC classification

Secondary: 34B16: Singular nonlinear boundary value problems 34B18: Positive solutions of nonlinear boundary value problems 34K13: Periodic solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 3 , June 2018 , pp. 605 - 617
Copyright
Copyright © Royal Society of Edinburgh 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)