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| Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems | |
| 引用本文： | Xiao-nlng Lin Hong Wang Da-qing Jiang. Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems[J]. 应用数学学报(英文版), 2007, 23(2): 289-302. DOI: 10.1007/s10255-007-0371-6 |
| 作者姓名： | Xiao-nlng Lin Hong Wang Da-qing Jiang |
| 作者单位： | Xiao-ning Lin School of Business，Northeast Normal University，Changchun 130024，ChinaHong Wang Department of Maths，Qiqihar University，Qiqihar 161006，ChinaDa-qing Jiang Department of Mathematics，Northeast Normal University，Changchun 130024，China |
| 基金项目： | Supported by Science Foundation for Young Teachers of Northeast Normal University （No： 20060108）, the National Natural Science Foundation of China （No. 10571021） and Key Laboratory for Applied Statistics of M0E（KLAS）. |
| 摘 要： | This paper is devoted to the study ofthe existence of single and multiple positive solutions forthe first order boundary value problem x′= f(t,x),x(0)=x(T),where f ∈ C([0,T]×R).In addition,weapply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at theorigin.Our proofs are based on a fixed point theorem in cones.Our results improve some recent results in theliteratures. |
| 关 键 词： | 一阶周期边值问题 正解 存在条件 非线性周期边值问题 |
| 修稿时间： | 2005-05-19 |
Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems |
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| Xiao-ning Lin,Hong Wang,Da-qing Jiang. Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems[J]. Acta Mathematicae Applicatae Sinica, 2007, 23(2): 289-302. DOI: 10.1007/s10255-007-0371-6 | |
| Authors: | Xiao-ning Lin Hong Wang Da-qing Jiang |
| Affiliation: | (1) School of Business, Northeast Normal University, Changchun, 130024, China;(2) Department of Maths, Qiqihar University, Qiqihar, 161006, China;(3) Department of Mathematics, Northeast Normal University, Changchun, 130024, China |
| Abstract: | Abstract This paper is devoted to the study of the existence of single and multiple positive solutions for the first order boundary value problem x′ = f(t, x), x(0) = x(T), where f ∈ C([0, T] × R) . In addition, we apply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at the origin. Our proofs are based on a fixed point theorem in cones. Our results improve some recent results in the literatures. Supported by Science Foundation for Young Teachers of Northeast Normal University (No: 20060108), the National Natural Science Foundation of China (No. 10571021) and Key Laboratory for Applied Statistics of MOE(KLAS) |
| Keywords: | Singular periodic boundary value problem single and multiple positive solution fixed point theorem in cones |
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