JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (10): 84-88.doi: 10.6040/j.issn.1671-9352.0.2016.610

Previous Articles     Next Articles

Periodic solutions for second order singular damped differential equations with a weak singularity

  

  1. 1. Teaching and Research Department of Basic Courses, Qinghai University, Xining 810016, Qinghai, China;
    2. College of Mathematics and Statistics, Qinghai Nationalities University, Xining 810007, Qinghai, China
  • Received:2016-12-30 Online:2017-10-20 Published:2017-10-12

PDF (PC)

367

Abstract: This article study some qualitative properties of the second order differential operator with periodic conditions, by using the Schauders fixed-point theorem. We obtained the existence of positive periodic solutions of a class of singular second-order damped differential equations. The conclusions in this paper perfect the existed results.

Key words: positive periodic solutions, damped, existence

CLC Number: 

  • O175.8
[1] LAZER A C, SOLIMINI S. On periodic solutions of nonlinear differential equations with singularities[J]. Proc Amer Math Soc, 1987, 99: 109-114.
[2] TORRES P J. Weak singularities may help periodic solutions to exist[J]. J Differential Equations, 2007, 232(1): 277-284.
[3] MA Ruyun, CHEN Ruipeng, HE Zhiqian. Positive periodic solutions of second-order differential equations with weak singularities[J]. Appl Math Comput, 2014, 232(23): 97-103.
[4] CAO Zhongwei, JIANG Daqing. Periodic solutions of seond order singular coupled systems[J]. Nonlinear Anal, 2009, 71(9): 3661-3667.
[5] 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: 643-662.
[6] CABDAD A, CID J Á. On the sign of the Greens function associated to Hills equation with an indefinite potential[J]. Appl Math Comput, 2008, 205(1): 303-308.
[7] LIU Bingmei, LIU Lishan, WU Yonghong. Existence of nontrivial periodic solutions for a nonlinear second order periodic boundary value problem[J]. Nonlinear Anal, 2010, 72(7-8): 3337-3345.
[8] ZHANG Zhongxin, WANG Junyu. On existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations[J]. J Math Anal Appl, 2003, 281(1): 99-107.
[9] LI Xiong, ZHANG Ziheng. Periodic solutions for second-order differential equations with a singular nonlinearity[J]. Nonlinear Anal, 2008, 69(11): 3866-3876.
[10] MA Ruyun. Nonlinear periodic boundary value problems with sign-changing Greens function[J]. Nonlinear Anal, 2011, 74(5): 1714-1720.
[11] MA Ruyun, XU Jia, HAN Xiaoling. Global bifurcation of positive solutions of a second-order periodic boundary value problem with indefinite weight[J]. Nonlinear Anal, 2011, 74: 3379-3385.
[12] HALK R, TORRES P J. Maximum and antimaximum principles for a second order differential operator with variable coefficients of indefinite sign[J]. Appl Math Comput, 2011, 217(19): 7599-7611.
[13] DEIMLING K. Nonlinear functional analysis [M]. Berlin: Springer, 1985.
[1] WANG Su-yun, LI Yong-jun. Solvability of nonlinear second-order boundary value problems with nonlinearities which cross the resonance points [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 53-56.
[2] . Existence of positive solutions for a class of nonlinear second-order Dirichlet problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 64-69.
[3] XIAO Xin-ling. Forward-backward stochastic differential equations on Markov chains [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 46-54.
[4] YE Fu-mei. Existence results of a resonance problem with derivative terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 25-31.
[5] ZHEN Wei-wei, ZENG Jian, REN Jian-long. Time dependent parabolic inverse source problem based on variational theory [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 61-71.
[6] ZHANG Sha, JIA Mei, LI Yan, LI Xiao-chen. Existence and uniqueness of solutions for three point boundary value problems of impulsive fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 66-72.
[7] WANG Shuang-ming. Dynamical analysis of a class of periodic epidemic model with delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(1): 81-87.
[8] CHEN Bin. Third-order periodic boundary value problems with sign-changing Greens function [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 79-83.
[9] SU Yan. Existence of solutions for second-order discrete Neumann problems at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 37-41.
[10] CHEN Bin, Abuelgasimalshaby Elzebir. Existence and multiplicity results for a second-order multi-point boundary value problem at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 49-52.
[11] CAI Chao. An inverse problem of identifying the coefficient in a Kolmogorov type equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 127-134.
[12] GUO Li-jun. Existence of positive solutions for a third-order three-point boundary value problem of nonlinear differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 47-53.
[13] ZHU Wen-wen. Existence and multiplicity of positive solutions of first order periodic boundary value problems with parameter [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 36-41.
[14] 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.
[15] WANG Xian-fei, JIANG Long, MA Jiao-jiao. Multidimensional backward doubly stochastic differential equations with generators of Osgood type [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(08): 24-33.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd