Báo Cáo Báo cáo hóa học AN ASYMPTOTIC RESULT FOR SOME DELAY DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLE

AN ASYMPTOTIC RESULT FOR SOME DELAY DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLE CH. G. PHILOS AND I. K. PURNARAS

Received 14 October 2003


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 characteristic 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.


1. Introduction and statement of the main result Difference equations with continuous variable are difference equations in which the unknown function is a function of a continuous variable.