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Asymptotic behaviour of solutions of higher order difference equations

100%

Migda M.

Demonstratio Mathematica

1998

tom Vol. 31, nr 1

71-80

On the asymptotic behaviour of solutions of nonlinear difference equations

100%

Migda M. , Schmeidel E.

Fasciculi Mathematici

2001

tom 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

100%

Migda M.

Fasciculi Mathematici

2001

tom 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.

Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations

75%

Graef J. R. , Thandapani E.

Fasciculi Mathematici

2001

tom Nr 31

23-36

The authors consider the nonlinear difference equation (E) delta2 ((delta(bn delta yn))+f(n,yn-t)=0, n należy N(no)={no,no+1,...}, here {an} and {bn} are positive real sequences, I is a nonnegative integer, f: N(no) x R R is a continuous function with uf(n, u) > 0 for all u nierówne 0. They obtain necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior. They also obtain sufficient conditions for all solutions to be oscillatory if/ is either strongly sublinear or strongly superlinear. Examples of their results are also included.

Nonexistence of global solutions to a class of nonlinear differential inequalities and application to hyperbolic-elliptic problems

63%

Alaa N. , Guedda M.

Journal of Applied Analysis

2003

tom Vol. 9, nr 1

103-121

We consider the problem [wzór] posed in Ω x (0,+∞). Here Ω ⊂ Rn is a an open smooth bounded domain and φ is like [wzór] and ε = š1. We prove, in certain conditions on f and φ that there is absence of global solutions. The method of proof relies on a simple analysis of the ordinary inequality of the type w'' + δw' ≥ αw + βwp. It is also shown that a global positive solution, when it exists, must decay at least exponentially.