二阶奇异耦合系统正周期解的存在性

doi:10.6040/j.issn.1671-9352.0.2014.578

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (10): 81-88.doi: 10.6040/j.issn.1671-9352.0.2014.578

二阶奇异耦合系统正周期解的存在性

吴成明

西北师范大学数学与统计学院, 甘肃兰州 730070

收稿日期:2014-12-22 修回日期:2015-04-21 出版日期:2015-10-20 发布日期:2015-10-21
作者简介:吴成明(1991-),男,硕士研究生,研究方向为常微分方程边值问题.E-mail:15294205595@163.com
基金资助:
国家自然科学基金资助项目(11361054);甘肃省自然科学基金资助项目(3ZS051-A25-016)

Existence of positive periodic solutions for second order singular coupled systems

WU Cheng-ming

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Received:2014-12-22 Revised:2015-04-21 Online:2015-10-20 Published:2015-10-21

摘要/Abstract

摘要： 运用Schauder不动点定理研究了二阶非自治奇异耦合系统

正周期解的存在性,其中a_i, e_i∈L¹(R/TZ, R), f_i∈Car(R/TZ×(0,∞), R),即f_i|_[0,T]:[0,T]×(0,∞)→R是L¹-Carathéodory函数(i=1, 2),并且f₁, f₂分别在y=0, x=0处允许有奇性。在扰动项积分值符号同正、同负和异号的情况下,分别获得了该奇异耦合系统存在正周期解的条件。

关键词: 正周期解, Schauder不动点定理, 弱奇异性, 奇异耦合系统

Abstract: Using Schauder's fixed point theorem, we study the existence of positive periodic solutions for second order non-autonomous singular coupled systems

where a_i, e_i∈L¹(R/TZ, R), f_i∈Car(R/TZ×(0,∞), R), that is, f_i|_[0,T]:[0,T]×(0,∞)→R are L¹-Carathéodory functions(i=1, 2), and f₁, f₂ may be singular at y=0, x=0, respectively. The existence of positive periodic solutions for the singular coupled systems are obtained under the conditions that the signs of integral disturbance terms are positive, or negative, or different.

Key words: positive periodic solutions, Schauder's fixed point theorem, weak singularity, singular coupled system

中图分类号:

O175.8

吴成明. 二阶奇异耦合系统正周期解的存在性[J]. 山东大学学报（理学版）, 2015, 50(10): 81-88.

WU Cheng-ming. Existence of positive periodic solutions for second order singular coupled systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 81-88.

参考文献

[1] TORRES P J. Weak singularities may help periodic solutions to exist[J]. J Differential Equations, 2007, 232(1):277-284.
[2] CHU Jifeng, TORRES P J. Applications of Schauder's fixed point theorem to singular differential equations[J]. Bull London Math Soc, 2007, 39(4):653-660.
[3] CHU Jifeng, LI Ming. Positive periodic solutions of Hill's equations with singular nonlinear perturbations[J]. Nonlinear Anal, 2008, 69(1):276-286.
[4] MA Ruyun, CHEN Ruipeng, HE Zhiqian. Positive periodic solutions of second-order differential equations with weak singularities[J]. Applied Mathematics and Computation, 2014, 232:97-103.
[5] O'REGAN D, WANG Haiyan. Positive periodic solutions of systems of second order ordinary differential equations[J]. Positivity, 2006, 10(2):285-298.
[6] CHU Jifeng, TORRES P J, ZHANG Meirong. Periodic solutions of second order non-autonomous singular dynamical systems[J]. J Differential Equations, 2007, 239(1):196-212.
[7] WANG Haiyan. Periodic solutions to non-autonomous second-order systems[J]. Nonlinear Anal, 2009, 71(3-4):1271-1275.
[8] CAO Zhongwei, JIANG Daqing. Periodic solutions of second order singular coupled systems[J]. Nonlinear Anal, 2009, 71(9):3661-3667.
[9] 姚庆六. 奇异二阶周期微分系统的正解[J]. 数学物理学报, 2012, 32A(3):576-587. YAO Qingliu. Positive solutions of singular second order periodic differential systems[J]. Acta Mathematica Scientia, 2012, 32A(3):576-587.
[10] TORRES P J. Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem[J]. J Differential Equations, 2003, 190(2):643-662.
[11] DEIMLING K. Nonlinear functional analysis[M]. Berlin: Springer, 1985.

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二阶奇异耦合系统正周期解的存在性

Existence of positive periodic solutions for second order singular coupled systems

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