Solvability of functional differential equations with multi-point boundary value problems at resonance

In this paper, we discuss the following third order functional differential equations subject to the boundary conditions where f:[0,1]×R6 R, F,G,H are three operators, , 0<η1<η2< <ηm−2<1. Under some appropriate conditions, some existence and multiplicity results are given for the problem at resonance by using a priori estimates and the topological degree theory of Mawhin.