Báo Cáo Báo cáo hóa học MAXIMUM PRINCIPLES FOR A FAMILY OF NONLOCAL BOUNDARY VALUE PROBLEMS PAUL

MAXIMUM PRINCIPLES FOR A FAMILY OF NONLOCAL BOUNDARY VALUE PROBLEMS PAUL W. ELOE Received 21 October 2003 and in revised form 16 February 2004

We study a family of three-point nonlocal boundary value problems (BVPs) for an nthorder linear forward difference equation. In particular, we obtain a maximum principle and determine sign properties of a corresponding Green function. Of interest, we show that the methods used for two-point disconjugacy or right-disfocality results apply to this family of three-point BVPs.

1. Introduction The disconjugacy theory for forward difference equations was developed by Hartman [15] in a landmark paper which has generated so much activity in the study of difference equations. Sturm theory for a second-order finite difference equation goes back to Fort [12], which also serves as an excellent reference for the calculus of finite differences. Hartman considers the nth-order linear finite difference equation Pu(m) = n j =0 α j (m)u(m + j) =