JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 79-83.doi: 10.6040/j.issn.1671-9352.0.2015.476

Previous Articles     Next Articles

Third-order periodic boundary value problems with sign-changing Greens function

CHEN Bin   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2015-10-16 Online:2016-08-20 Published:2016-08-08

Abstract: We study the existence of positive solutions of nonlinear periodic boundary value problemsu(t)+a(t)u(t)=λb(t)f(u(t)), a.e t∈[0,2π],u(i)(0)=u(i)(2π), i=0,1,2where a≺0, b≺0 and the Greens function of the linear problemu(t)+a(t)u(t)=0, a.e t∈[0,2π],u(i)(0)=u(i)(2π), i=0,1,2may change sign on [0,2π]×[0,2π].

Key words: positive periodic solution, sign-changing Greens function, Schauder fixed point theorem, existence

CLC Number: 

  • O175.8
[1] CHU Jifeng, ZHOU Zhongcheng. Positive solutions for singular non-linear third-order periodic boundary value problems[J]. Nonlinear Analysis, 2006, 64(7):1528-1542.
[2] LI Yongxiang. Positive periodic solutions for fully third-order ordinary differential equations[J]. Computers and Mathematics with Applications, 2010, 59(11):3464-3471.
[3] ZEHOUR B, ABDELKADERl B, SIDI M. Existence result for impulsive third order periodic boundary value problems[J]. Applied Mathematics and Computation, 2008, 206(2):728-737.
[4] FENG Yuqiang. On the existence and multiplicity of positive periodic solutions of a nonlinear third-order equation, 2009, 22(8):1220-1224.
[5] KONG Lingbin, WANG Shoutian, WANG Junyu. Positive solution of a singular nonlinear third-order periodic boundary value problem[J]. Journal of Computational and Applied Mathematics, 2005, 132(2):247-253.
[6] YU Hengxue, PEI Minghe. Solvability of a nonlinear third-order periodic boundary value problem[J]. Applied Mathematics Letters, 2010, 23(8):892-896.
[7] MUKHIGULASHVILI S. On a periodic boundary value problem for third order linear functional differential equations[J]. Nonlinear Analysis, 2007, 66(2):527-535.
[8] MA Ruyun. Nonlinear periodic boundary value problems with sign-changing Greens function[J]. Nonlinear Analysis, 2011, 74(5): 1714-1720.
[9] CAC N, GATICA J, LI Yi. Positive solutions to semilinear problems with coefficient that changes sign[J]. Nonlinear Analysis, 1999, 34(4):501-510.
[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] . Periodic solutions for second order singular damped differential equations with a weak singularity [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 84-88.
[8] 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.
[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!