[PDF] Top 20 Asymptotic Behavior of Solutions for Linear Implicit Difference Equations with Index 1

... in implicit difference equations (IDEs) (also referred to as singular difference equations, discrete-time descriptor systems) because of their appearance in many practical areas, such ... See full document

... differential-difference equations of Volterra type are often used to model biological populations, see [13, 16, ...of linear Volterra difference equations of both convolution and nonconvolution types ... See full document

... the asymptotic properties of the solutions of second order differential equations [1] [2] difference equ- ations of the type (E) and/or related equations have been investigated ... See full document

... for solutions to a special summation equation and a first order nonlinear difference equation which will be often used ...> 1. The next paper Error bounds for asymptotic solutions of ... See full document

... and asymptotic behavior of solutions of neutral difference equations, see [1]-[5], and the references cited ...and asymptotic behavior of solu- tions of neutral ... See full document

... After, we have studied the existence of convergent solutions of nonlinear systems whose linear part has a dichotomy See 13, 14, 16-18] These results are obtained under absolutely summabl[r] ... See full document

... The cherry on the cake could be the classroom note [21] by Brand (1955) published in a widely read popular journal, which solves the bilinear difference equation in the way as it was suggested by old French masters [6, ... See full document

... the linear difference equation, where one of the coefficients is periodic or con- stant and the others asymptotically approach zero, and obtained sufficient conditions for the existence of asymptotically periodic ... See full document

... Zeng, Asymptotic behavior for non-oscillatory solutions of difference equations with several delays in the neutral term, Journal of Applied Mathematics and Computing, ...No. 1– ... See full document

... whose solutions, as one can easily check, are also solutions of the problem (), because the convergence of the series is implicitly assumed in this ...the solutions to problem () are also ... See full document

... Consequently, under (4.6), (4.7), and (4.8), our main result says that 0 is an asymp- totically stable equilibrium for the method (4.2) with probability one. Thus, this extends results for the linear case (cf. [9, ... See full document

... Notice that system (1.1), in some cases, can have equilibrium points which belong to the coordinate axes as, for instance, when a = 0 and/or d = 0. As we mentioned earlier, the case a = d = 0 has been considered in ... See full document

... Difference equations have many applications in applied sciences, there are many papers and books that can be found concerning the theory and applications of difference equations, see ... See full document

... the asymptotic theory of the solutions of Volterra difference equations is extensive, and application of this theory is rapidly increasing to various ...difference equations, we choose to refer ... See full document

... Equation 1 is locally asymptotically ...Equation 1 is global attractor. In Sect. 4 we give the solutions of some special cases of Equation 1 and give a numerical exam- ples of each case and ... See full document

... of solutions of (1.1) in the cases of global asymptotic stability ...local behavior implies the global behavior for competitive linear fractional ... See full document

... Difference equations appear naturally as discrete analogues and in the numerical solutions of differential and delay differential equations, and they have applications in biology, ecology, physics, and ... See full document

... good deal of attention in the literature, and for recent results of this type, we refer the reader to the monographs of Agarwal [1], Agarwal and Wong [2] as well as the papers of Cheng et al. [3], Graef et al. ... See full document

... We turn to the proof of Theorem .. We use the integral estimate () to show the ex- istence of nontrivial blow-up nonnegative solutions, while we construct some global self- similar supersolutions to show the ... See full document

... Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation dut/dt + Aut+ Gut ft, where A is a maximal monotone operator in a nilbert spa[r] ... See full document