[PDF] Top 20 On a k Order System of Lyness Type Difference Equations

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2007, Article ID 31272, 13 pages doi 10 1155/2007/31272 Research Article On a k Order System of Lyness Type Difference Equations[.] ... See full document

... to system () to the periodic one is essentially used a related stronger condition to (), for which there is not needed any fixed point theorem, but just some ... See full document

... where k, l ∈ N , k = l, min { α, r} > , and p ≥ , which was proposed for studying by Stević at numerous ...related equations has been studied considerably (see, for example, [, , , , –, ... See full document

... where f (x) is continuous on R and satisfies the signum condition xf (x) > 0 if x = 0. The obtained results are best possible in a certain sense. Proof is given by means of the Riccati technique and phase plane ... See full document

... Leray-Schauder type fixed point theorem, which states that a compact mapping T has a fixed point if it satisfies the Leray-Schauder boundary condition on B(, R), for some R > , that is, if there exists R >  ... See full document

... difference equations and systems not stemming from differential ones (see, ...difference equations and systems has re-attracted recent attention (see, ...complicated equations and systems into simpler ... See full document

... difference equations and systems have been investigated in the last twenty years ...difference equations and systems, but without mentioning any theory, have ... See full document

... In order to verify our theoretical results and to support our theoretical discussions, we consider several interesting numerical examples in this ...the system of nonlinear difference equations ... See full document

... ficient conditions on the existence of nontrivial homoclinic solutions that have both of the components not identically zero to system (.), in [] and []. However, we find that no similar results were obtained ... See full document

... difference equations of type (1.4;δ), the study of higher-order equations, and in particular third-order equations of type ...for equations with deviating ... See full document

... The oscillatory behavior of difference equations has been intensively studied in recent years. Most of the literature has been concerned with equations of type (1.1) with l = 1 (see [1–10] and ... See full document

... Difference equations usually describe the evolution of some certain phenomena over time and are also important in describing dynamics for fundamentally discrete system, see ... See full document

... Many types of difference equations and systems have been studied so far. A part of the studies can be found in [–]. Some types of the systems essentially obtained by sym- metrization of scalar ones were studied ... See full document

... ference equations often plays a critical role in studying the stability behavior of their so- lutions; see [, , ...third-order Lyness difference equation under quadratic ... 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

... difference equations such as oscillation theory, disconjugacy, and eigenvalue problems (see [1, 2, 5–7, 9, 13, 15, 21, 24, 27–29, 37, 39, 45, 48, 57, 59] and the references ... 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

... however, no significant progress took place on this line. Recently, equation () was recon- sidered and its inverse was defined by – , and many interesting results in applications such as in number theory as well as in ... See full document

... The discrete boundary value problems have been studied by many authors. Some ex- istence results were obtained by using various methods [–]. For example, using the method of upper and lower solutions and the cone ... See full document

... difference equations on an axis and a half-axis, and we establish a correspondence between such equations and simpler kinds of operator ...operator equations can be solved by a special method like the ... See full document