依赖于一阶导数的(n-1,1)共轭m点边值问题正解的存在性

纪玉德; 郭彦平; 禹长龙

依赖于一阶导数的(n-1,1)共轭m点边值问题正解的存在性

河北科技大学理学院,石家庄 050018

基金项目: 河北省自然科学基金资助项目(A2006000298)

详细信息

作者简介:
纪玉德(1979- ),男,内蒙古赤峰人,讲师,硕士(联系人.E-mail:jiyude-1980@163.com).

中图分类号: O175.8
计量
- 文章访问数: 3258
- HTML全文浏览量: 148
- PDF下载量: 780
- 被引次数: 0
出版历程
- 收稿日期: 2008-04-10
- 修回日期: 2009-02-14
- 刊出日期: 2009-04-15

Positive Solutions for(n-1,1) m-Point Boundary Value Problems With Dependence on the First Order Derivative

College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, P. R. China

摘要

摘要: 利用锥上的Krasnoselskii's不动点定理的推广定理,讨论了一类边值问题，给出了相应依赖于一阶导数的非线性n阶m点边值问题至少一个正解的存在性．对于n阶m点边值问题，给出了相应的Green函数,证明了在非线性项f满足一定的增长条件下至少存在1个正解．并且给出了一个例子来说明所获得的结果．
- Green函数 /
- 锥上的不动点定理 /
- 正解 /
- 高阶微分方程
Abstract: Using the extension of Krasnoselskii's fixed point theorem in a cone,the existence of at least one positive solution to the nonlinear n th order m-point boundary value problem with dependence on the first order derivative was proved.The associated Green's function for the n th order mpoint boundary value problem was given,and growth conditions were imposed on nonlinear term f which ensure existence of at least one positive solutions.A simple example was presented to illustrate applications of the obtained results.
- Green’s function /
- fixed point theorem in a cone /
- positive solution /
- highe-rorder differential equation

HTML全文

参考文献(11)

[1]	l'in V A,Moiseev E I.Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator[J].Differential Equations,1987,23(8):979-987.
[1]	l'in V A,Moiseev E I.Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects[J].Differential Equations,1987,23(7):803-810.
[3]	MA Ru-yun. Positive solutions of a nonlinear three-point boundary value problems[J]. Electronic Journal of Differential Equations,1999,34(4):1-8.
[4]	MA Ru-yun. Existence theorems for a second order m-point boundary value problems[J]. J Math Anal Appl,1997,211(2):545-555. doi: 10.1006/jmaa.1997.5416
[5]	MA Ru-yun. Positive solutions for second order three-point boundary value problems[J]. Applied Mathematics Letters,2001,14(1):1-5. doi: 10.1016/S0893-9659(00)00102-6
[6]	MA Ru-yun. Existence theorems for a second order three-point boundary value problems[J]. J Math Anal Appl,1997,212(2):430-442. doi: 10.1006/jmaa.1997.5515
[7]	LIU Xiu-jun,QIU Ji-qing,GUO Yan-ping. Three positive solutions for second-order m-point boundary value problems[J]. Applied Mathematics and Computation,2004,156(3):733-742. doi: 10.1016/j.amc.2003.06.021
[8]	GUO Yan-ping,SHAN Wen-rui,GE Wei-gao. Positive solutions for second-order m-point boundary value problems[J]. Journal of Computational and Applied Mathematics,2003,151(2):415-424. doi: 10.1016/S0377-0427(02)00739-2
[9]	GUO Yan-ping,GE Wei-gao.Positive solutions for three-point boundary value problems with dependence on the first order derivatives[J]. J Math Anal Appl,2004,290(1):291-301. doi: 10.1016/j.jmaa.2003.09.061
[10]	Eloe Paul W,Ahmad Bashir. Positive solutions of a nonlinear nth boundary value problems with nonlocal conditions[J]. Applied Mathematics Letters,2005,18(5):521-527. doi: 10.1016/j.aml.2004.05.009
[11]	Eloe Paul W,Henderson Johnny. Positive solutions for (n-1,1) conjugate boundary value problems[J].Nonlinear Anal,1997,28(10):1669-1680. doi: 10.1016/0362-546X(95)00238-Q