| 一类非线性分数阶微分方程边值问题的正解 |
| |
| 引用本文： | 郭建敏,张雅平,康淑瑰.一类非线性分数阶微分方程边值问题的正解[J].数学的实践与认识,2013,43(11). |
| |
| 作者姓名： | 郭建敏 张雅平 康淑瑰 |
| |
| 作者单位： | 大同大学数学与计算机科学学院,山西大同,037009 |
| |
| 基金项目： | 国家自然基金,山西大同大学科研基金,山西省高校科技开发基金 |
| |
| 摘 要： | 讨论以下非线性分数阶边值问题:cD_(0+)cD_(0+)αu(t)+λa(t)f(u(t))=0,0cD_(0+)cD_(0+)α是Caputo导数,λ>0.利用Krasnoselskiis不动点定理,得到其正解存在与不存在的充分条件,最后给出一个例子验证我们的结论.
|
| 关 键 词： | 分数阶微分方程 边值问题 正解 不动点定理 |
Positive Solutions for Boundary Value Problems of Nonlinear Fractional Differential Equation |
| |
| GUO Jian-min
,
ZHANG Ya-ping
,
KANG Shu-gui.Positive Solutions for Boundary Value Problems of Nonlinear Fractional Differential Equation[J].Mathematics in Practice and Theory,2013,43(11). |
| |
| Authors: | GUO Jian-min ZHANG Ya-ping KANG Shu-gui |
| |
| Abstract: | In this paper,we investigate the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem:~cD_(0+)~α+u(t) +λa(t) f(u(t)) = 0,0 < t < 1 u(o) = u'(1) = u"(0) = 0,where 2 <α≤3 is a real number and ~c D_(0+)~αis the standard Caputo differentiation.λ> 0.Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators.An example is also given to illustrate the main results. |
| |
| Keywords: | fractional differential equation boundary value problem positive solution fixed point theroem |
| 本文献已被 万方数据 等数据库收录！ |
|
