Nontrivial Solutions for a Class of Fractional Differential Equations with Integral Boundary Conditions and a Parameter in a Banach Space with Lattice

Existence of nontrivial solutions for the following fractional differential equation with integral boundary conditions D(0+)(alpha)u(t) + h(t)f (t, u (t)) = 0, 0 < t < 1, u(0) = u'(0) = u ''(0) = 0, u(1) = lambda integral(eta)(0) u(s)ds is investigated by using results for the computation of topological degree under the lattice structure, where 3 < alpha <= 4, 0 < eta <= 1, 0 <= lambda eta(alpha)/alpha < 1, D-0+(alpha) is the standard Riemann-Liouville derivative. h(t) is allowed to be singular at t = 0 and t = 1.