Multiple positive solutions for (n-1, 1)-type semipositone conjugate boundary value problems of nonlinear fractional differential equations

In this paper, we consider (n-1, 1)-type conjugate boundary value problem for the nonlinear fractional differential equation D0+u(t) + λf(t, u(t)) = 0, 0 < t < 1, λ > 0, u(0) = 0, 0 ≤ j ≤ n − 2, u(1) = 0, where λ is a parameter, α ∈ (n − 1, n] is a real number and n ≥ 3, and D0+ is the Riemann-Liouville’s fractional derivative, and f is continuous and semipositone. We give properties of Green’s function of the boundary value problems, and derive an interval of λ such that any λ lying in this interval, the semipositone boundary value problem has multiple positive solutions.