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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:

𝐃 0 ν +u(t)+h(t)f(t,u(t))=0,0<t<1,n-1<νn,u(0)=u ' (0)==u (n-2) (0)=0,𝐃 0+ α u(t)] t=1 =0,1αn-2,

where n and 𝐃 0 ν + is the standard Riemann-Liouville fractional derivative of order ν. 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:
34A08Fractional differential equations
34B18Positive solutions of nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
References:
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