[PDF] Top 20 Global Behavior of Solutions to Two Classes of Second Order Rational Difference Equations

... whose dynamics differ significantly from other equations in this class. There are a total of 42 cases that arise from 1.1 in the manner just discussed, under the hypotheses B C > 0 and α β γ > 0. The recent ... See full document

... difference equations, although their forms (or expressions) look very simple, it is extremely difficult to understand thoroughly the global behaviors of their ... See full document

... Although difference equations are sometimes very simple in their forms ,they are extremely difficult to understand thoroughly the behavior of their solutions ...studied global ... See full document

... qualitative behavior of difference equations and systems is a topic of great ...difference equations have appeared recently in many areas such as ecology, population dynamics, queuing problems, ... See full document

... nonlinear rational difference equations of a higher order is quite challenging and rewarding, and the results about these equations offer prototypes towards the development of the basic ... See full document

... Equation (1.3) was studied in detail in [7, 10], where we have found the region of param- eters for which the equilibrium is globally asymptotically stable and the region where the equation has a unique period-two ... See full document

... When δ = 1, equation (1) has been considered in [17] and [19]. When δ = 1 and ∇ F(n, x) = 0, equation (1) has been also studied. For example, in [1] and [8], the authors were interested in the results on disconjugacy, ... See full document

... [8] studied the global behavior of positive solution to the fourth-order rational difference equations.. Although difference equations are sometimes very simple in their forms, they are [r] ... See full document

... difference equations can be useful in their ...several classes of difference equations and systems of difference equations can be found, ...general solutions to some classes of ... See full document

... past two decades, the study of Difference Equations has been growing ...that difference equations appear as mathematical models describing real life situations in probability theory, ... See full document

... Definition 2.3:The essential fact which distinguishes time series data from other statistical data in the specific order in which observations are taken. While observations from areas other than time series are ... See full document

... periodic solutions of second-order difference equations have been studied by many authors, see ...periodic solutions of the ... 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 difference ... See full document

... This paper is divided into four parts. First of all, Section 2 states some basic notations and presents variational structure. Second, in Section 3, we shall state and prove our main results by using the ... See full document

... in difference equation representation. Here a special type of difference equation satisfied by three asymptotic sequences may be takes as a representation of a complexity issues in the computation of ... See full document

... asymptotic behavior at infinity of increasing positive solutions of second order quasilinear ordinary differential equations (p(t) ϕ (x (t))) + q(t) ψ (x(t)) = 0 are studied in the ... See full document

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

... Necessary and su ffi cient conditions for regular or slow variation of all positive solutions of a second-order linear difference equation with arbitrary sign coefficient are established. Relations with ... See full document

... of equations began with the paper of Lazer and Solimini [], in which the authors provide necessary and sufficient conditions for the existence of periodic solutions of the ... See full document

... We obtain a sufficient condition for the existence of periodic and subharmonic solutions of second-order p-Laplacian di ff erence equations using the critical point theory. Copyright © 2007 P. ... See full document