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Zbl 1182.34005
Mena, J.Caballero; Harjani, J.; Sadarangani, K.
Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems. (English)
[J] Bound. Value Probl. 2009, Article ID 421310, 10 p. (2009). ISSN 1687-2770/e

From the introduction: We discuss the boundary-value problem $$\aligned & D_{0^+}^\alpha,u(t)+f(t,u(t))=0,\quad 0<t<1,\\ & u(0)=u'(1)=u''(0)=0,\endaligned\tag*$$ where $2<\alpha\le 3$, $D_{0^+}^\alpha$ is the Caputo's differentiation and $f:(0,1]\times [0,\infty)\to [0,\infty)$ with $\lim_{t\to 0^+}f(t,-)=\infty$ (i.e., $f$ is singular at $t=0$). We prove the existence and uniqueness of a positive and nondecreasing solution for the problem (*) by using a fixed point theorem in partially ordered sets.

MSC 2000:: *34A08
34B15 Nonlinear boundary value problems of ODE
47N20 Appl. of operator theory to differential and integral equations

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Zentralblatt MATH Berlin [Germany]