An asymptotic result for some delay difference equations with continuous variable

Ch G Philos, IK Purnaras
2004 Advances in Difference Equations  
We consider a nonhomogeneous linear delay difference equation with continuous variable and establish an asymptotic result for the solutions. Our result is obtained by the use of a positive root with an appropriate property of the so-called characteristic equation of the corresponding homogeneous linear (autonomous) delay difference equation. More precisely, we show that, for any solution, the limit of a specific integral transformation of it, which depends on a suitable positive root of the
more » ... acteristic equation, exists as a real number and it is given explicitly in terms of the positive root of the characteristic equation and the initial function.
doi:10.1155/s1687183904310058 fatcat:xob3362gonfl7pv654qdrnaisu