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

Abstract

Existence of nontrivial solutions for the following fractional differential equation with integral boundary conditions D0+αu(t)+h(t)f(t,u(t))=0, 0<t<1, u(0)=u'(0)=u′′(0)=0, u(1)=λ∫0ηu(s)ds is investigated by using results for the computation of topological degree under the lattice structure, where 3<α≤4, 0<η≤1, 0≤ληα/α<1, D0+α is the standard Riemann-Liouville derivative. h(t) is allowed to be singular at t=0 and t=1.