JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (10): 81-88.doi: 10.6040/j.issn.1671-9352.0.2014.578

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Existence of positive periodic solutions for second order singular coupled systems

WU Cheng-ming   

  1. 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

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Abstract: Using Schauder's fixed point theorem, we study the existence of positive periodic solutions for second order non-autonomous singular coupled systems
                                                             
where ai, ei∈L1(R/TZ, R), fi∈Car(R/TZ×(0,∞), R), that is, fi|[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

CLC Number: 

  • O175.8
[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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