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Uniqueness of positive solutions for a class of fractional boundary value problems. (English) Zbl 1247.34011
Summary: The work is concerned with the existence and uniqueness of positive solutions for the following fractional boundary value problem: $$\cases \bold D^\nu_0+u(t)+h(t)f(t,u(t))=0, \quad 0<t<1,n-1<\nu\leq n, &\\ u(0)=u'(0)=\cdots=u^{(n-2)}(0)=0, &\\ [\bold D^\alpha_{0+}u(t)]_{t=1}=0, \quad 1\leq \alpha \leq n-2, \endcases$$ where $n \in \Bbb N$ and $\bold D^\nu_0+$ is the standard Riemann-Liouville fractional derivative of order $\nu$. Our main results are formulated in terms of spectral radii of some related linear integral operators, and the nonlinearity $f$ is considered to grow only sublinearly.

##### MSC:
 34A08 Fractional differential equations 34B18 Positive solutions of nonlinear boundary value problems for ODE 47N20 Applications of operator theory to differential and integral equations
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##### References:
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