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On the asymptotic behaviour of solutions to a linear functional equation

Sokołowski D.

Opuscula Mathematica

2012

Vol. 32, no. 3

559-577

We investigate the asymptotic behaviour at infinity of solutions of the equation [formula].We show among others that, under some assumptions, any positive solution of the equation which is integrable on a vicinity of infinity or vanishes at +∞ tends on some sequence to zero faster than some exponential function, but it does not vanish faster than another such function.

On the asymptotic behaviour of solutions of nonlinear difference equations

Migda M., Schmeidel E.

Fasciculi Mathematici

2001

Nr 31

63-69

This paper consists of three theorems. For the nonlinear difference equation (E) wzór sufficient conditions for the existence of the asymptotically constant solutions are given in Th. 1. In Th. 2 conditions under which there exists a solution (xn) of Eq. (E) such that xn = cn + o(1), are given. In Th. 3 conditions under which every solution (xn) of Eq. (E) possesses property: the sequence (xn/n is convergent in R, are presented.

Asymptotic behaviour of solutions of nonlinear delay difference equations

Migda M.

Fasciculi Mathematici

2001

Nr 31

57-62

Asymptoic properties of the solutions of the difference equation of the form ^(r(n-1)^x(n-1))+anf(x(n-k)=bn are studied.