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

Published online by Cambridge University Press:  10 May 2018

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

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018 

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