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Existence and Boundary Behavior of Positive Solutions for a Semilinear Fractional Differential Equation
Journal article   Peer reviewed

Existence and Boundary Behavior of Positive Solutions for a Semilinear Fractional Differential Equation

Habib Maagli, Majda Chaieb, Abdelwaheb Dhifli and Samia Zermani
Mediterranean journal of mathematics, Vol.12(4), pp.1265-1285
01/11/2015
DOI: https://doi.org/10.1007/s00009-015-0571-x

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We consider the following semilinear fractional initial value problem D alpha u(x) = a(x)u(sigma) (x), x is an element of (0, 1) and lim(x -> 0) x(1-alpha)u(x) = 0, where and a is a positive measurable function on (0, 1). We establish the existence and the uniqueness of a positive solution in the space of weighted continuous functions. We also give the boundary behavior of such solution.

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