No abstract

No abstract

Abstract. New explicit stability results are obtained for the following scalar linear difference equationand for some nonlinear Volterra difference equations.

Abstract. We consider the nonlinear discrete Volterra equations of non-convolution typeWe present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, especially asymptotically polynomial and asymptotically periodic solutions. We use o(n s ), for a given nonpositive real s, as a measure of approximation. We also give conditions under which all solutions are asymptotically polynomial.

No abstract

No abstract

We consider a class of fourth-order nonlinear difference equations. The classification of nonoscillatory solutions is given. Next, we divide the set of solutions of these equations into two types: F + -and F − -solutions. Relations between these types of solutions and their nonoscillatory behavior are obtained. Necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties.

We consider the nonlinear difference equationwhere {a n }, {b n }, {q n } are positive real sequences, f is a real function with xf (x) > 0 for all x = 0. We obtain sufficient conditions for the boundedness of all nonoscillatory solutions of the above equation. Some examples are also given.