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

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

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 ([email protected])
Zaitao Liang
Affiliation:
Department of Mathematics, College of Science, Hohai University, Nanjing 210098, People's Republic of China
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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 

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