J4 ›› 2010, Vol. 45 ›› Issue (8): 81-86.

• Articles • Previous Articles     Next Articles

Existence of solutions for a discrete three-point boundary value problems at resonance

CHEN Tian-lan   

  1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2009-12-22 Online:2010-08-16 Published:2010-09-16


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.

Key words: resonance problem; lower and upper solutions; connectivity of the solution sets; existence

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