Positive solutions for a class of fractional 3-point boundary value problems at resonance
Tóm tắt
In this paper, we study the nonlocal fractional differential equation:
$$\left \{ \textstyle\begin{array}{@{}l} D^{\alpha}_{0+}u(t)+f(t,u(t))=0 ,\quad 0< t< 1,\\ u(0)=0,\qquad u(1)=\eta u(\xi), \end{array}\displaystyle \right . $$
where
$1 < \alpha< 2$
,
$0 < \xi< 1$
,
$\eta\xi^{\alpha-1}= 1$
,
$D^{\alpha}_{0+}$
is the standard Riemann-Liouville derivative,
$f:[0,1]\times[0,+\infty)\rightarrow\mathbb{R}$
is continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique.
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