Attractivity and global stability for linearizable difference equations

Global Attractivity in Nonlinear Delay Difference Equations

We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation x„+l = x„f(xn_k), n = 0,1,2,..., are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model JVI+i = aN¡/(\ +ßNt_k) and to the delay difference equation xn+i = x„er^~x"-k'1 .

Stability and Global Attractivity for a Class of Nonlinear Delay Difference Equations

where c ∈ [0,1) is a given constant, k is a positive integer, f : R→ R is continuous and f (0)= 0, f (u) = 0 for u = 0. Such a equation arises from some of the earliest mathematical models of the macroeconomic “trade cycle,” and have attracted a great deal of attention (see, e.g., [1, 4, 5, 6, 7, 8, 9, 10] and references cited therein). When k = 1, Sedaghat [9] obtained some sufficient conditio...

Global Attractivity of a Family of Max-Type Difference Equations

On Global Attractivity of a Class of Nonautonomous Difference Equations

We mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by yn p ryn−s / q φn yn−1, yn−2, . . . , yn−m yn−s , n ∈ N0, with p ≥ 0, r, q > 0, s,m ∈ N and positive initial values, and present some sufficient conditions for the parameters andmaps φn : R m → R , n ∈ N0, under which every positive solution to the equation converges to zero or a u...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...