非线性分数阶微分方程的一个正解
On a Positive Solution to Nonlinear Fractional Differential Equations
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摘要: 讨论了非线性分数阶微分方程Da0+u(t)+f(t,u(t))=0(t∈(0,1))在Dirichlet边值条件u(0)=u(1)=0下正解的存在性,其中α∈(1,2],Dα0+是标准的Riemann-Liouville微分,f:[0,1]×[0,+∞)→[0,+∞)连续.利用不动点指数理论,在f关于u次线性的条件下,得到边值问题至少存在一个正解.
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关键词:
- 分数阶微分方程 /
- Dirichlet边值问题 /
- 正解 /
- 不动点指数理论
Abstract: This paper discusses the existence of positive solutions to nonlinear fractional differential equation Da0+u(t)+f(t, u(t))=0(t∈(0, 1)) subject to Dirichlet boundary value condition u(0)=u(1)=0, where α∈(1, 2], Dα0+ is the standard Riemann-Liouville differentiation, and f: [0, 1]×[0, +∞)→[0,+∞) is continuous.According to the fixed point index theory, the existence results of at least one positive solution are obtained under the condition that f is sublinear on u. -
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