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Zbl 1247.34011
Xu, Jiafa; Wei, Zhongli; Dong, Wei
Uniqueness of positive solutions for a class of fractional boundary value problems. (English)
[J] Appl. Math. Lett. 25, No. 3, 590-593 (2012). ISSN 0893-9659

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 2000:: *34A08
34B18 Positive solutions of nonlinear boundary value problems
47N20 Appl. of operator theory to differential and integral equations

Keywords: fractional boundary value problem; spectral radii; positive solution; fixed point index

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