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Triple Solutions for a Higher-order Difference Equation  
 
  Authors: Zengji Du, Chunyan Xue, Weigao Ge,  
  Keywords: Discrete three-point boundary value problem; Multiple solutions; Green's function; Cone; Fixed point.  
  Date Received: 09/04/04  
  Date Accepted: 24/12/04  
  Subject Codes:

39A10.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

In this paper, we are concerned with the following $ n$th difference equations

$displaystyle Delta ^{n}y(k-1)+f(k,y(k))=0,   kin {1,dots ,T}, $

$displaystyle Delta ^{i}y(0)=0,i=0,1,dots ,n-2,    Delta ^{n-2}y(T+1)=alpha Delta ^{n-2}y(xi ), $

where $ f$ is continuous, $ ngeq 2$, $ Tgeq 3$ and $ xi in {2,dots ,T-1}$ are three fixed positive integers, constant $ alpha>0$ such that $ alpha xi T+1$. Under some suitable conditions, we obtain the existence result of at least three positive solutions for the problem by using the Leggett-Williams fixed point theorem.;


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