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

Alaa N., Guedda M.

Journal of Applied Analysis

2003

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.

Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations

Graef J. R., Thandapani E.

Fasciculi Mathematici

2001

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.

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.

Asymptotic behaviour of solutions of higher order difference equations

Migda M.

Demonstratio Mathematica

1998

Vol. 31, nr 1

71-80