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Uniqueness and asymptotic behavior of positive solutions for a fractional-order integral boundary value problem. (English) Zbl 1253.35201
Summary: We study a model arising from porous media, electromagnetic, and signal processing of wireless communication system -𝒟 t α x(t)=f(t,x(t),x ' (t),x '' (t),,x (n-2) (t)), 0<t<1, x(0)=x ' (0)==x (n-2) (0)=0, x (n-2) (1)= 0 1 x (n-2) (s)dA(s) where n-1<αn, n, and n2,𝒟 t α is the standard Riemann-Liouville derivative, 0 1 x(s)dA(s) is the linear functional given by the Riemann-Stieltjes integrals, A is a function of bounded variation, and dA can be a changing-sign measure. The existence, uniqueness, and asymptotic behavior of positive solutions to the singular nonlocal integral boundary value problem for fractional differential equation are obtained. Our analysis relies on Schauder’s fixed-point theorem and upper and lower solution method.
MSC:
35R11Fractional partial differential equations
35B40Asymptotic behavior of solutions of PDE
35B09Positive solutions of PDE
35A02Uniqueness problems for PDE: global uniqueness, local uniqueness, non-uniqueness