Existence and asymptotic behavior of positive solutions for semilinear fractional Navier boundary-value problems
Date
2017-05-25
Authors
Maagli, Habib
Dhifli, Abdelwaheb
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the existence, uniqueness, and asymptotic behavior of positive continuous solutions to the fractional Navier boundary-value problem
Dβ(Dαu)(x) = -p(x)uσ, ∈ (0, 1),
lim x→0 x1-β Dαu(x) = 0, u(1) = 0,
where α, β ∈ (0, 1] such that α + β > 1, Dβ and Dα stand for the standard Riemann-Liouville fractional derivatives, σ ∈ (-1, 1) and p being a nonnegative continuous function in (0, 1) that may be singular at x = 0 and satisfies some conditions related to the Karamata regular variational theory. Our approach is based on the Schäuder fixed point theorem.
Description
Keywords
Fractional Navier differential equations, Dirichlet problem, Positive solution, Asymptotic behavior, Schäuder fixed point theorem
Citation
Mâagli, H., & Dhifli, A. (2017). Existence and asymptotic behavior of positive solutions for semilinear fractional Navier boundary-value problems. <i>Electronic Journal of Differential Equations, 2017</i>(141), pp. 1-13.
Rights
Attribution 4.0 International