Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences
Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences
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DOI：
10.1007/s12190-012-0551-2
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发表时间：
2012-03
影响因子：
2.2
通讯作者：
Sihua Liang;Jihui Zhang
中科院分区：
文献类型：
--
作者：
Sihua Liang;Jihui Zhang
本文考虑如下非线性q-分数阶三点边值问题$$\开始{array}{l}（D_{q}^{\alpha}u）（t）+ f（t，u（t））=0，\quad 0 < t < 1，2 < \alpha< 3，\\ [2pt]u（0）=（D_qu）（0）= 0，\quad（D_qu）（1）= \beta（D_qu）（\eta），\end{array}$$其中0<βηα-2 <$1。利用偏序集上的一个不动点定理，得到了上述边值问题存在唯一正解和非减解的充分条件。
In this paper, we consider the following nonlinearq-fractional three-point boundary value problem $$\begin{array}{l}(D_{q}^{\alpha}u)(t) + f(t,u(t))=0, \quad 0 < t < 1, 2 < \alpha< 3,\\ [2pt]u(0) = (D_qu)(0) = 0, \quad(D_qu)(1) = \beta(D_qu)(\eta),\end{array}$$ where 0<βηα-2<1. By using a fixed-point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solutions to the above boundary value problem.