Resumen de Existence of Solution for a p-Laplacian Multi-point Boundary Value Problem at Resonance

Xiaojie Lin, Qin Zhang

• In this paper, we are concerned with the p-Laplacian multi-point boundary value problem (ϕp(x′′(t)))′=f(t,x(t),x′(t),x′′(t)),t∈(0,1),ϕp(x′′(0))=∑i=1mαiϕp(x′′(ξi)),x′(1)=∑j=1nβjx′(ηj),x′′(1)=0,where ϕp(s)=|s|p-2s,p>1,ϕq=ϕp-1,1p+1q=1,f:[0,1]×R3→R is a continuous function, 0<ξ1<ξ2<⋯<ξm<1,αi∈R,i=1,2,…,m,m≥2 and 0<η1<⋯<ηn<1,βj∈R,j=1,…,n,n≥1. Based on the extension of Mawhin’s continuation theorem, a new general existence result of the p-Laplacian problem is established in the resonance case.