On the existence of solutions of pp-Laplacian mm-point boundary value problem at resonance

By using the theory of coincidence degree, we study a kind of solutions of pp-Laplacian mm-point boundary value problem at resonance in the following form View the MathML source{(ϕp(u′))′(t)=f(t,u,u′),00(i=1,2,…,m−2),0<ξ1<ξ2<⋯<ξm−2<1 such that View the MathML source∑i=1m−2ai=1. A result on the existence of solutions is obtained. The degrees of two variables x1,x2x1,x2 in the function f(t,x1,x2)f(t,x1,x2) are allowable to be bigger than 1.