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

Autor: Abdelwaheb Dhifli, Samia Zermani, Habib Mâagli, Majda Chaieb
Rok vydání: 2015
Předmět:
Zdroj: Mediterranean Journal of Mathematics. 12:1265-1285
ISSN: 1660-5454
1660-5446
DOI: 10.1007/s00009-015-0571-x
Popis: We consider the following semilinear fractional initial value problem $$D^{\alpha} u(x) = a(x)u^{\sigma} (x), x\in (0, 1) \quad {\rm and} \quad \lim\limits_{x \longrightarrow0^{+}}x^{1 - \alpha} u(x) = 0,$$ where \({0 < \alpha < 1, \sigma < 1}\) 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.
Databáze: OpenAIRE
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