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 $D_{0+}^{\alpha }u(t)+h(t)f(t,u(t))=0$, , $u(0)=u\text{'}(0)=u^{\prime \prime }(0)=0$, $u(1)=\lambda {\int }_0^{\eta }u(s)\text{d}s$ is investigated by using results for the computation of topological degree under the lattice structure, where , , , $D_{0+}^{\alpha }$ is the standard Riemann-Liouville derivative. $h(t)$ is allowed to be singular at $t=0$ and $t=1$.