Maagli, HabibDhifli, Abdelwaheb2022-05-232022-05-232017-05-25Mâagli, 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. 1-13.1072-6691https://hdl.handle.net/10877/15798We 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.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalFractional Navier differential equationsDirichlet problemPositive solutionAsymptotic behaviorSchäuder fixed point theoremArticle