ANZIAM  J.  47 (2005), 237-248
A boundary value problem for second-order nonlinear difference equations on the integers

F. Dal
  Department of Mathematics
  Ege University
  35100 Bornova
  Izmir
  Turkey
 
and
G. Sh. Guseinov
  Department of Mathematics
  Atilim University
  06836 Incek
  Ankara
  Turkey
    guseinov@atilim.edu.tr


Abstract
In this study, we are concerned with a boundary value problem (BVP) for nonlinear difference equations on the set of all integers $\mathbb{Z}$, under the assumption that the left-hand side is a second-order linear difference expression which belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space $\ell^2$ and includes boundary conditions at infinity. Existence and uniqueness results for solution of the considered BVP are established.
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