含p-Laplace算子的Sturm-Liouville边值问题正解的性质

杨景保

doi:10.21656/1000-0887.370047

含p-Laplace算子的Sturm-Liouville边值问题正解的性质

doi: 10.21656/1000-0887.370047

杨景保

亳州学院教育系,安徽亳州 236800

基金项目: 安徽省高校自然科学研究项目（KJ2013B153；KJ2013Z218）；安徽省专业带头人资助项目

详细信息

作者简介:
杨景保（1968—），男，教授，硕士（E-mail: jbyang1@126.com）.

中图分类号: O175.8
计量
- 文章访问数: 1074
- HTML全文浏览量: 88
- PDF下载量: 646
- 被引次数: 0
出版历程
- 收稿日期: 2016-02-13
- 修回日期: 2016-04-20
- 刊出日期: 2016-08-15

Properties of Positive Solutions to Sturm-Liouville Boundary Value Problems With p-Laplace Operators

YANG Jing-bao

Department of Education, Bozhou University, Bozhou, Anhui 236800, P.R.China

摘要

摘要: 研究了含p-Laplace算子的Sturm-Liouville边值问题正解的性质.利用p-Laplace算子的性质，使用L’Hôpital（洛必达）法则和闭区间上连续函数的最值性定理，研究了含p-Laplace算子的Sturm-Liouville边值问题，得到了其正解存在的两个必要条件.最后给出了主要结论的应用.结论丰富了边值问题研究领域的内容，为利用计算机使用迭代技术求这类边值问题的近似解提供了新的渠道，推广了一些文献的结论.
- p-Laplace算子 /
- Sturm-Liouville边值问题 /
- 最值性定理
Abstract: The properties of positive solutions were investigated for a class of SturmLiouville boundary value problems with p-Laplace operators. Based on the properties of p-Laplace operators, and according to the L’H?pital’s rule and the extreme value theorem for continuous functions on closed intervals, the SturmLiouville boundary value problems with p-Laplace operators were studied. The 2 necessary conditions for the existence of positive solutions were obtained. In the last part, the application of the main findings was given. The work enriches the content in the field of boundary value problems, and provides a new channel of using computer and iterative techniques to find approximate solutions to boundary value problems, meanwhile extending some conclusions in previous literatures.
- p-Laplace operator /
- Sturm-Liouville boundary value problem /
- extreme value theorem

HTML全文

参考文献(14)

[1]	缪烨红, 张吉慧. 三点边值问题的正解[J]. 应用数学和力学, 2008,29(6): 741-748.(MIAO Ye-hong, ZHANG Ji-hui. Positive solutions of three-point boundary value problems[J]. Applied Mathematics and Mechanics,2008,29(6): 741-748.(in Chinese))
[2]	TAN Hui-xuan, FENG Han-ying, FENG Xing-fang, DU Ya-tao. Triple positive solutions to a third-order three-point boundary value problem with p-Laplacian operator[J].Chinese Quarterly Journal of Mathematics,2015,30(1): 55-65.
[3]	苏华, 刘立山. 变号(k,n-k)共轭边值问题解的存在问题[J]. 数学学报(中文版), 2015,58(2): 261-270.(SU Hua, LIU Li-shan. The solutions for semipositone (k,n-k) conjugate boundary value problems[J].Acta Mathematica Sinica(Chinese Series),2015,58(2): 261-270.(in Chinese))
[4]	张海娥. 带Riemann-Stieljes积分条件的三阶边值问题的单调正解[J]. 应用数学和力学, 2015,36(7): 779-786.(ZHANG Hai-e. Multiple monotone positive solutions to 3rd-order boundary value problems involving Riemann-Stieltjes integral conditions[J].Applied Mathematics and Mechanics,2015,36(7): 779-786.(in Chinese))
[5]	刘洋, 刘志辉, 李诚志, 胡卫敏. 一类具有分数阶导数项的分数阶微分方程边值问题多重正解的存在性[J]. 数学的实践与认识, 2016,46(4): 242-249.(LIU Yang, LIU Zhi-hui, LI Cheng-zhi, HU Wei-min. Existence of solutions for multi-point boundary value problems for fractional differential equations[J].Mathematics in Practice and Theory,2016,46(4): 242-249.(in Chinese))
[6]	WANG Qi, WANG Mei. Existence of three solutions for boundary value problem involving p-Laplacian[J].Mathematica Applicata,2016,29(1): 194-198.
[7]	Lü Hai-shen, BAI Zhan-bing. A necessary and sufficient condition for the existence of positive solutions to the singularp -Laplacian [J]. Acta Analysis Functionalis Applicata,2004,6(4): 289-296.
[8]	李华, 仉志余. 带p-Laplace算子的非线性两点边值问题正解存在的充分必要条件[J]. 徐州师范大学学报(自然科学版), 2008,26(2): 33-35.(LI Hua, ZHANG Zhi-yu. A necessary and sufficient condition for the existence of positive solutions for the nonlinear two-point boundary value problem withp -Laplacian[J].Journal of Xuzhou Normal University(Natural Science Edition),2008,26(2): 33-35.(in Chinese))
[9]	YANG Chen, YAN Ju-rang. Positive solutions for third-order Sturm-Liouville boundary value problems withp -Laplacian[J].Computers & Mathematics With Applications,2010,59(6): 2059-2066.
[10]	FENG Xing-fang, FENG Han-ying, TAN Hui-xuan. Existence and iteration of positive solutions for third-order Sturm-Liouville boundary value problems withp -Laplacian[J].Applied Mathematics and Computation,2015,266(1): 634-641.
[11]	SUN Bo, GE Wei-gao.Existence and iteration of positive solutions to a class of Sturm-Liouville-like p-Laplacian boundary value problems[J].Nonlinear Analysis: Theory, Methods & Applications,2008,69(4): 1454-1461.
[12]	LI Zhi-yan, YAN Shu-lin, GE Wei-gao. Multiple positive solutions to a nonlinear two-point boundary value problem with p-Laplacian[J].Journal of Mathematical Research and Exposition,2006,26(3): 480-488.
[13]	杨景保. 一类Sturm-Liouville边值问题正解的存在性[J]. 山东大学学报(理学版), 2010,45(2): 84-89.(YANG Jing-bao. Existence of positive solutions for a class of Sturm-Liouville boundary value problems[J].Journal of Shandong University(Natural Science),2010,45(2): 84-89.(in Chinese))
[14]	华东师范大学数学系. 数学分析[M]. 北京: 高等教育出版社, 2001.(Department of Mathematics of East China Normal University.Mathematical Analysis [M]. Beijing: Higher Education Press, 2001.(in Chinese))