Two positive solutions for (n - l,l)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations

摘要

In this paper, we consider the (n - 1,1 )-type integral boundary value problem of nonlinear fractional differential equation D~α_0+u(t) + λf(r, v(t)) = 0, 0 < t < 1 D~α_0+v(t) + λg(t,u(t)) = 0, u~0)(0) = v~0)(0) = 0, 0≤j≤n-2, u(l) = μf~1_0 u(s)ds. v(1) = μf~1_0v(s)ds, where λ, μ are parameter and 0 < μ < a, a e (n - 1, n] is a real number and n ≥ 3, D~α_0, is the Riemann-Liouville's fractional derivative, /, g are continuous and semipositone. We gave the corresponding Green's function for the boundary value problem and its some properties. Moreover, we derive an interval of /. such that any I lying in this interval, the semipositone boundary value problem has multiple positive solutions.