Solvability of multipoint boundary value problems at resonance for higher-order ordinary differential equations,

Let f : [0, 1]× Rn → R be a continuous function and e L1[0, 1]. Let βj (1 ≤ j ≤ m − 2) R, 0 < η1 < η2 < … < ηm−2 < 1 be given. This paper is concerned with the existence of solutions for the following nth-order multipoint boundary value problems at resonance case x(n)(t)=f(t,x(t),x′(t),…,x(n−1)(t))+e(t),t (0,1), and x(n)(t)=f(t,x(t),x′(t),…,x(n−1)(t))+e(t),t (0,1), Some existence results are obtained by using the coincidence degree theory of Mawhin.