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mawhin's continuation theorem

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Positive periodic solutions for singular fourth-order differential equations with a deviating argument
Part of
- Functional-differential and differential-difference equations
- Boundary value problems
Fanchao Kong, Zaitao Liang
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 3 / June 2018

Published online by Cambridge University Press:

10 May 2018, pp. 605-617

Print publication:

June 2018
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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.