%A CHEN Tian-lan %T Existence of solutions for a discrete three-point boundary value problems at resonance %0 Journal Article %D 2010 %J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) %R %P 81-86 %V 45 %N 8 %U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_1872.shtml} %8 2010-08-16 %X

The existence of solutions are discussed for the secondorder difference equation threepoint boundary value problems
Δ2u(t-1)=f(t, u(t)),t∈T,
u(0)=εΔu(0), u(T+1)=αu(η),
where f: T×R→R is continuous, T is a fixed positive integer, T:={1, 2,…,T}. And ε∈[0,∞), α∈(0,∞), η∈T  are given constants such that α(η+ε)=T+1+ε. The proof of our main results is based on the method of lower and upper solutions using the connectivity properties of the solution sets of parameterized families of compact vector fields.