Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation

By using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equation D-0+(alpha) u(t) + lambda a(t) f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) = Sigma(infinity)(i=1) alpha(i)u(xi(i)) are considered, where 1 < alpha <= 2 is a real number, lambda is a positive parameter, D-0+(alpha) is the standard Riemann- Liouville differentiation, and xi(i) is an element of (0, 1), alpha(i) is an element of [0,infinity) with Sigma(infinity)(i-1)alpha(i)xi(alpha-1)(i) < 1, a(t) is an element of C([0, 1], [0,infinity)), f(t, u) is an element of C([0,infinity), [0,infinity)).