Abstract: This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance {(Φp (x’))’ + f(t,x)=0,0 < t < 1,...,0 < ξ < 1. An existence theorem is obtained by using the extension of Mawhin’s continuation theorem. Since almost all the multi-point boundary value problem at resonance in previous papers are for the linear operator without p-Laplacian by the use of Mawhin’s continuation theorem, our method is new. 

Key words: multi-point boundary value problem, the extension of Mawhin’s continuation