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

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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

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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.
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