上下解方法与三点边值共振问题的可解性

J4 ›› 2008, Vol. 43 ›› Issue (5): 66-70 .doi:

上下解方法与三点边值共振问题的可解性

徐玲

西北师范大学数学与信息科学学院, 甘肃兰州 730070

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 徐玲

Methods of lower and upper solutions and the solvability of a three-point boundary value problem at resonance

XU Ling

College of Mathematics and Information Science, Northwest Normal University,Lanzhou 730070, Gansu, China

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: XU Ling

摘要/Abstract

摘要：

运用紧向量场方程的解集连通理论为二阶三点边值共振问题
u″(t)=f(t,u(t),u′(t)),t∈［0, 1］,
u′(0)=0,u(1)=u(η)
发展上下解方法, 其中常数η∈(0, 1), 函数f:［0, 1］×R2→R连续且满足Nagumo条件。

关键词: 连通集; 上下解; 共振; 存在性

Abstract:

The methods of lower and upper solutions for a second order three-point boundary value problem at resonance
u″(t)=f(t, u(t), u′(t)), t∈［0, 1］,
u′(0)=0, u(1)=u(η)
were developed by using the connectivity properties of the solution sets of parameterized families of compact vector fields, where η∈(0, 1), f:［0, 1］×R2→R is continuous and satisfies the Nagumo condition.

Key words: connected sets; lower and upper solutions; resonance; existence

中图分类号:

O175.8

徐玲 . 上下解方法与三点边值共振问题的可解性[J]. J4, 2008, 43(5): 66-70 .

XU Ling . Methods of lower and upper solutions and the solvability of a three-point boundary value problem at resonance[J]. J4, 2008, 43(5): 66-70 .

参考文献

相关文章 8

[1]	李凡凡,刘锡平*,智二涛. 分数阶时滞微分方程积分边值问题解的存在性[J]. J4, 2013, 48(12): 24-29.
[2]	俎冠兴. 边值问题的多重正解[J]. J4, 2009, 44(12): 71-76.
[3]	姚庆六. 一类奇异次线性Sturm Liouville 边值问题[J]. J4, 2009, 44(10): 36-38.
[4]	许万银. 一类拟线性Neumann问题的多重解[J]. J4, 2009, 44(10): 39-42.
[5]	代丽美. 正指数Emden-Fowler方程脉冲奇异边值问题的PC¹(［0,1］,R₊)正解[J]. J4, 2008, 43(12): 10-14.
[6]	续晓欣梁月亮桑彦彬. 三阶两点边值问题单调递减正解的存在惟一性[J]. J4, 2008, 43(12): 84-87.
[7]	唐秋云,王明高,刘衍胜 . 高阶p-Laplacian算子方程组边值问题多个正解的存在性[J]. J4, 2008, 43(5): 50-53 .
[8]	秦小娜,贾梅*,刘帅. 具Caputo导数分数阶微分方程边值问题正解的存在性[J]. J4, 2013, 48(10): 62-67.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed