Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable

摘要

In this paper, we consider the following higher-order semipositone nonlocal Riemann-Liouville fractional differential equation D_(0+)~α x(t) + f(t, x(t),D_(0+)~β x(t)) + e(t) = 0, 0 < t < 1,D_(0+)~βx(0) = D_(0+)~(β+1) x(0) = ??? = D_(0+)~(n+β?2) x(0) = 0, and D_(0+)~βx(1) = Σ_(i=1)~(m?2) η_iD_(0+)βx(ξ_i), where D_(0+)~α and D_(0+)~β are the standard Riemann-Liouville fractional derivatives. The existence results of positive solution are given by Guo-krasnosel’skii fixed point theorem and Schauder’s fixed point theorem.