《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (12): 32-37.

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### 带积分边界条件的四阶边值问题的单调正解

1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
• 发布日期:2019-12-11
• 作者简介:何燕琴(1994— ), 女, 硕士研究生,研究方向为常微分方程边值问题. E-mail:1193360529@qq.com*通信作者简介:韩晓玲(1978— ),女,教授,博士生导师,研究方向为常微分方程边值问题. E-mail:hanxiaoling9@163.com
• 基金资助:
国家自然科学基金资助项目(11561063)

### Monotone positive solutions of fourth-order boundary value problems with integral boundary conditions

HE Yan-qin, HAN Xiao-ling*

1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
• Published:2019-12-11

Abstract: By using the monotone iterative technique, this article studies the existence of monotone positive solutions for fourth order boundary value problems with integral boundary conditions{u(4)(t)=f(t,u(t),u'(t)), t∈(0,1),u(0)=u'(1)=u(1)=0,u″(0)=∫10g(t)u″(t)dt,where f:［0,1］×［0,+∞)2→［0,+∞) is continuous, g:［0,1］→［0,+∞) is continuous, not only the existence of the positive solution of the problem is obtained, but also the initial value of the iterative sequence is a simple zero function or a primary function.

• O175.8
 [1] 孙建平, 靳存程. 带积分边界条件的三阶边值问题的单调正解[J]. 兰州大学学报(自然科学版), 2012, 48(5):98-101. SUN Jianping, JIN Cuncheng. Monotone positive solution of third order boundary value problems with integral boundary conditions[J]. Journal of Lanzhou University(Natural Sciences), 2012, 48(5):98-101.[2] 廉玉婷, 高云兰, 李晓宇. 一类奇异三阶微分方程三点边值问题正解的存在性[J]. 内蒙古工业大学学报(自然科学版), 2015, 34(2):87-91. LIAN Yuting, GAO Yunlan, LI Xiaoyu. The existence of positive solutions for three point boundary value problems of singular third order differential equations[J]. Journal of Inner Mongolia University of Technology(Natural Sciences Edition), 2015, 34(2):87-91.[3] AMANN H. Fixed point equations and nonlinear eigenvalue problems in oedered Banach spaces[J]. SIAM Review, 1976, 18(4):620-709.[4] LV Xuezhe, WANG Libo, PEI Minghe. Monotone positive solution of a fourth-order BVP with integral bounday condition[J]. Boundary Value Problems, 2015, 172(2):1-12.[5] ZHANG Xuemei, GE Weigao. Symmetric positive solutions of boundary value problems with integral boundary conditions[J]. Applied Mathematics and Computation, 2012, 219(8):3553-3564.[6] PEI Minghe, CHANG Sungkag. Monotone iterative technique and symmetric positive solutions for a fourth-order boundary value problem[J]. Mathematical and Computer Modelling, 2010, 51(9):1260-1267.[7] FENG Hanying, JI Dehong, GE Weigao. Existence and uniqueness of solutions for a fourth-order boundary value problem[J]. Nonlinear Analysis, 2009, 70(10):3561-3566.[8] ALBERTO C,WANG Guotao. Positive solutions of nonlinear fractional differential equations with integral boundary value conditions[J]. Journal of Mathematical Analysis and Applications, 2012, 389(1):403-411.[9] YUAN Chengjun, JIANG Daqing. Existence and uniqueness of positive solutions for fourth-order nonlinear singular continuous and discrete boundary value problems[J]. Applied Mathematics and Computation, 2018, 203(1):194-201.[10] 闫平. 带积分边界条件的四阶边值问题正解存在性[J]. 甘肃科学学报, 2013, 25(3):9-12. YAN Ping. The existence of positive solutions for fourth order boundary value problems with integral boundary conditions[J]. Journal of Gansu Sciences, 2013, 25(3):9-12.
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