| 一类离散m点边值问题正解的存在性和多重性 |
| |
| 引用本文： | 秦发金,姚晓洁,朱宝骧.一类离散m点边值问题正解的存在性和多重性[J].大学数学,2007,23(5):50-55. |
| |
| 作者姓名： | 秦发金 姚晓洁 朱宝骧 |
| |
| 作者单位： | 柳州师范高等专科学校,数计系,广西,柳州,545004;柳州师范高等专科学校,数计系,广西,柳州,545004;柳州师范高等专科学校,数计系,广西,柳州,545004 |
| |
| 摘 要： | 运用锥拉伸与锥压缩的Krasnosel’skii不动点定理,讨论了一类离散m点边值问题Δ2u(k)+λa(k)f(u(k))=0,k∈N,Δu(0)=∑m-2i=1biΔu(li),u(T+2)=∑m-2i=1aiu(li).在不要求极限li mu→0f(u)u,lui→m∞f(uu)存在的情形下,得到了其正解的存在性、非存在性和多重性的充分条件,推广了文1]的相应结果.
|
| 关 键 词： | 离散m点边值问题 正解 存在性 非存在性 多解性 不动点定理 |
| 文章编号： | 1672-1454（2007）05-0050-06 |
| 修稿时间： | 2005-12-17 |
Existence and Multiplicity of Positive Solutions for Discrete m-Point Boundary Value Problems |
| |
| QIN Fa-jin,YAO Xiao-jie,ZHU Bao-xiang.Existence and Multiplicity of Positive Solutions for Discrete m-Point Boundary Value Problems[J].College Mathematics,2007,23(5):50-55. |
| |
| Authors: | QIN Fa-jin YAO Xiao-jie ZHU Bao-xiang |
| |
| Institution: | Department of Mathematics and Computer Science, Liuzhou Teachers College, Liuzhou, Guangxi 545004, China |
| |
| Abstract: | By applying the Krasnosel'skii fixed point theorem on cone expansion and compression type,we obtain the existence,nonexistence and multiplicity of positive solutions for discrete m-point boundary value problemsΔ2u(k)+λa(k)f(u(k))=0,k∈N,Δu(0)=∑m-2i=1biΔu(li),u(T+2)=∑m-2i=1aiu(li).while limu→0f(u)u and limu→∞f(u)u are not required to exist,the main result of 1] is extended. |
| |
| Keywords: | discrete m-points boundary value problems positive solution existence nonexistence multiplicity solutions fixed point theorem |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
