摘要
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,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),where βi∈ R,m-3 ∑i=1 β i=1,0 < η 1 < η 2 < ··· < ηm-3 < 1,m-3 ∑i=1 βiηi=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.
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,x＇ （0）=x＇（ξ） x（1）=m-3 ∑i=1 βi x（η i）,where βi ∈ R,m-3 ∑i=1 β i=1,0 η 1 η 2 … ηm-3 1,m-3 ∑i=1 βi ηi=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.
