JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (10): 33-39.doi: 10.6040/j.issn.1671-9352.0.2019.031

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Existence of positive solutions for boundary value problems of third-order delay differential equations

LUO Qiang, HAN Xiao-ling*, YANG Zhong-gui   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-10-12

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Abstract: By applying the fixed point theorem on the cone, this paper studies the existence of positive solutions for boundary value problems of third-order delay differential equation{u(t)+λa(t)f(t,u(t-τ))=0, t∈(0,1),τ>0,u(t)=0,-τ≤t≤0,u(0)=u″(0)=0,u(1)=αu(η)where λ is parameter, and 0<η<1, 0<α<1/η, f:［0,1］×［0,∞］→［0,∞) is continuous.

Key words: delay differential equation, boundary value problem, positive solution, existence, fixed point theorem

CLC Number: 

  • O175.8
[1] HU Peng, HUANG Chengming. Delay dependent stability of stochastic split-step θ methods for stochastic delay differential equations[J]. Applied Mathematical and Computation, 2018, 339(24): 663-674.
[2] 张长沐. 三阶微分方程三点边值问题正解的存在性[J]. 山东师范大学学报(自然科学版), 2017, 32(2): 30-34. ZHANG Changmu. Existence of positive solution for three-point boundary value problem of third-order differential equations[J]. Journal of Shandong Normal University(Natural Science), 2017, 32(2): 30-34.
[3] 田德生. 一类二阶时滞微分方程多个周期解的存在性[J]. 应用数学学报, 2016, 39(4): 537-546. TIAN Desheng. Existence of multiple periodic solutions for a second-order delayed differential equation[J]. Acta Mathematicae Applicatae Sinica, 2016, 39(4): 537-546.
[4] 郭丽君. 非线性微分方程三阶三点边值问题正解的存在性[J]. 山东大学学报(理学版), 2016, 51(12): 47-53. GUO Lijun. 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.
[5] 杨甲山. 具可变时滞的二阶非线性中立型泛函微分方程的振动性[J]. 浙江大学学报(理学版), 2016,43(3): 257-263. YANG Jiashan. Oscillation of certain second-order nonlinear neutral functional differential equations with variable delay[J]. Journal of Zhejiang University(Science Edition), 2016, 43(3): 257-263.
[6] TAN Yanxiang, HUANG Chuangxia, SUN Bo. Dynamics of a class of delayed reaction-diffusion systems with Neumann boundary condition[J]. Journal of Mathematical Analysis and Applications, 2018, 458(2): 1115-1130.
[7] ZUO Wenjie, SONG Yongli. Stability and bifurcation analysis of a reaction-diffusion equation with spatio-temporal delay[J]. Journal of Mathematical Analysis and Applications, 2015, 430(1): 243-261.
[8] AVUDAI S P, RAMANUJAM N. A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition[J]. Applied Mathematical and Computation, 2017, 296(5): 101-115.
[9] ZHAO Jingjun, FAN Yan, XU Yang. An analysis of delay-dependent stability of symmetric boundary value methods for the linear neutral delay integro-differential equations with four parameters[J]. Applied Mathematical Modelling, 2015, 39(9): 2453-2469.
[10] 张晓建. 二阶Emden-Fowler型变时滞中立型微分方程的振荡性[J]. 浙江大学学报(理学版), 2018, 45(3): 308-313. ZHANG Xiaojian. Oscillation of second-order Emden-Fowler type variable delay neutral differential equation[J]. Journal of Zhejiang University(Science Edition), 2018, 45(3): 308-313.
[11] 郭大钧. 非线性泛函分析[M]. 济南: 山东科学技术出版社, 1985. GUO Dajun. Nonlinear functional analysis[M]. Jinan: Shandong Science and Technology Press, 1985.
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