Existence of solutions for singular fractional Navier boundary value problems

摘要

In this paper, we are concerned with the following fractional Navier boundary value problem: Dβ (Dαu)(x) = ?g(u), x ∈ (0, 1), lim x→0+ x 1?βDαu(x) = ?a, u(1) = b, where α, β ∈ (0, 1] such that α + β > 1, Dα and Dβ stand for the standard Riemann-Liouville fractional derivatives, the function g is continuous and nonincreasing on (0, ∞) and the reals a, b ∈ (0, ∞). Using Sch¨auder’s fixed point theorem, we prove the existence of positive continuous solutions.