Abstract
We consider the following semilinear fractional system
{D(alpha)u = p(t)u(a)v(r) in (0,1),
D(beta)v = q(t)u(s)v(b) in (0,1),
lim(t -> 0+) t(1-alpha) u(t) = lim(t -> 0+) t(1-beta)v(t) = 0,
where alpha, beta is an element of (0, 1), a, b is an element of (-1,1), r, s is an element of R such that (1 - vertical bar a vertical bar)(1 - vertical bar b vertical bar) - vertical bar rs vertical bar > 0, D-alpha, D-beta are the Riemann-Liouville fractional derivatives of orders alpha, beta and the nonlinearities p, q are positive measurable functions on (0, 1). Applying the Schfiuder fixed point theorem, we establish the existence and the boundary behaviour of positive solutions in the space of weighted continuous functions.