Some higher-order multi-point boundary value problem at resonance

This paper deals with the existence of solutions for the following nth order multi-point boundary value problem at resonancex(n)(t)=f(t,x(t),x′(t),…,x(n-1)(t))+e(t),t∈(0,1),x(0)=∑i=1m-2αix(ξi),x′(0)=⋯=x(n-2)(0)=0,x(1)=x(η),where f:[0,1]×Rn⟶R is a continuous function, e∈L1[0,1], αi∈R(1⩽i⩽m-2), 0<ξ1<ξ2<⋯<ξm-2<1 and 0<η<1. An existence theorem is obtained by using the coincidence degree theory of Mawhin.