[PDF] Top 20 On the oscillation of solutions for a class of second order nonlinear stochastic difference equations

... the solutions to deterministic difference equations has been discussed in many ...the oscillation of the solutions to deterministic difference ...the solutions to stochastic ... See full document

... Proposition A. Equation (.) can be classified into two types as follows. (i) If λ > /, then all nontrivial solutions of equation (.) are oscillatory. (ii) If λ ≤ /, then all nontrivial solutions ... See full document

... the oscillation of solutions for different classes of second order dif- ferential ...the oscillation problem for ...the nonlinear equations with damping ... See full document

... u (or u m ,n < 0 ) for large numbers m and n . It is said to be oscillatory if it is neither eventually positive nor eventually negative. (1) is called oscillatory if all of its nontrivial solutions are ... See full document

... first order equations whose oscillatory behaviors are already ...the oscillation of all solutions of ...wide class of nonlinear second order difference ... See full document

... We shall consider only nontrivial solutions of Equa- tion (1.1) which are defined for all large t. A solution of Equation (1.1) is said to be oscillatory if it has arbitrarily large zeros, otherwise it is said to ... See full document

... If all solutions of Eq. (1.1) are oscillatory, then Eq. (1.1) is said to be oscillatory. Before given the main results, we note that the initial value problem which consists of Eq. (1.1) and the initial function ... See full document

... of solutions of various classes of second order nonlinear difference equations, see [1, 2, 10, 12] and the references contained ...the oscillation of ... See full document

... few oscillation results are known for forced equations (see [5, 6, 7, 8, 9, 10, ...all solutions of (1) are oscillatory under the influence of certain classes of forcing ... See full document

... The aim of this section is to study non-oscillatory solutions of (). If (S) has a solution (x, y, z, w), then (–x, –y, –z, –w) is a solution of (S), too. Hence, when studying the non- existence conditions for ... See full document

... difference equations with many examples in applications such as asymptotic behavior of solutions of difference equations were studied extensively by Elaydi [] where the analytic and geometric ... See full document

... differential equations is an important branch of differential ...the oscillation theory of impulsive differential equations emerging as an important area of research, since such equations have ... See full document

... SZMANDA, B., Oscillation Theorems for Nonlinear Second-order Difference Equations, J.. Li, Z.H., A Note on the Oscillatory Property for Nonlinear Difference Equations and Differentlal Eq[r] ... See full document

... 0, n ∈ Z, 1.5 has been studied. Other interesting contributions can be found in some recent papers 7–11 and in references contained therein. It is interesting to study second-order nonlinear ... See full document

... Theorem . (Nonlinear alternative for single-valued maps []) Let E be a Banach space, let C be a closed and convex subset of E, and let U be an open subset of C and  ∈ U. Suppose that F : U → C is a ... See full document

... determining oscillation theorem for second order nonlinear difference equation has been the subject of investigation in ...linear difference equations of second ... See full document

... In this paper, we shall investigate some oscillation criteria for the solutions of mth-order nonlinear neutral difference equation where m ≥ 1. The results presented here complement some of the ... See full document

... difference equations and systems, it should be tried to transfer a problem to equivalent one, if possible, or, at least, as long as it is ...general solutions to difference equations; see, for example, ... See full document

... Now we introduce an operator which divides the set of solutions of a special case of (1.1) into two disjoint subsets. We will prove that, for nonoscillatory solution, the first of them equals type (ii) solution ... See full document

... of second-order rational difference ...oscillatory solutions of this equation, and the positive equilibrium point 1 of this equation is proved to be globally asymptotically ... See full document