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

被引：4

作者：

Kong, Fanchao ^{[1
,3
]}

Liang, Zaitao ^{[2
,3
]}

机构：

[1] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China

[2] Hohai Univ, Dept Math, Coll Sci, Nanjing 210098, Jiangsu, Peoples R China

[3] Anhui Univ Sci & Technol, Sch Math & Big Data, Huainan 232001, Anhui, Peoples R China

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2018年 / 148卷 / 03期

关键词：

positive periodic solutions; fourth-order differential equations; Mawhin's continuation theorem; deviating argument; singularity; EXTENDED FISHER-KOLMOGOROV; BOUNDARY-VALUE-PROBLEMS; EIGENVALUE;

D O I：

10.1017/S030821051800001X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the singular fourth-order differential equation with a deviating argument: x((4))(t) + f(x(t))x'(t) + g(t, x(t - tau)) = e(t). 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 = infinity, which is different from the known ones in the literature.

引用

页码：605 / 617

页数：13

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