[1]马陆一,闫东亮,李晓燕*.非线性一阶周期边值问题解的分歧结构[J].四川师范大学学报(自然科学版),2017,(04):478-481.[doi:10.3969/j.issn.1001-8395.2017.04.008 ]
 MA Luyi,YAN Dongliang,LI Xiaoyan.Bifurcation Structure of Nonlinear First-order Periodic Boundary Value Problems[J].Journal of SichuanNormal University,2017,(04):478-481.[doi:10.3969/j.issn.1001-8395.2017.04.008 ]
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非线性一阶周期边值问题解的分歧结构()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2017年04期
页码:
478-481
栏目:
基础理论
出版日期:
2017-04-30

文章信息/Info

Title:
Bifurcation Structure of Nonlinear First-order Periodic Boundary Value Problems
文章编号:
1001-8395(2017)04-0478-04
作者:
马陆一 闫东亮 李晓燕*
西北师范大学 数学与统计学院, 甘肃 兰州 730070
Author(s):
MA Luyi YAN Dongliang LI Xiaoyan
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu
关键词:
分歧理论 一阶周期边值问题 多解性
Keywords:
bifurcation theory first-order periodic boundary value problem multiplicity results
分类号:
O175.8
DOI:
10.3969/j.issn.1001-8395.2017.04.008
文献标志码:
A
摘要:
在λ=0附近解的个数的变化情况,其中h∈C[0,T]且∫T0h(s)ds=0,非线性函数f∈C([0,T]×[WT5"HZ]R[WT5"BZ],[WT5"HZ]R[WT5"BZ])并满足广义符号条件,T>0,λ∈[WT5"HZ]R[WT5"BZ]是一个参数.证明存在λ+,λ->0,当λ∈[0,λ+]时,该问题至少有一个解;当λ∈[-λ-,0)时,该问题至少有3个解.
Abstract:
In this paper, we use bifurcation theory and continuation theory to show the multiplicity results for first-order periodic boundary value problem {u'+λu+f(t,u)=h(t), t∈[0,T], u(0)=u(T), where h∈C[0,T] and ∫T0h(s)ds=0; f∈C([0,T]×R,R)and satisfies the generalized sign condition, T>0, λ∈R is a parameter. We show that there exist λ+, λ_>0,R)and satisfies the generalized sign condition, T>0, λ∈R is a parameter. We show that there exist uch that this problem has at least one solution if λ∈[0,λ+] and has at least three solutions if λ∈[-λ_,0).

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2016-03-29
基金项目:国家自然科学基金(11671322)
*通信作者简介:李晓燕(1979—),女,讲师,主要从事常微分方程边值问题的研究,E-mail:lixydodo@163.com
更新日期/Last Update: 2017-04-30