Global stability for nonlinear difference equations with variable coefficients

Abstract

Consider the following nonlinear difference equation with variable coefficients:

New global stability conditions for a class of difference equations

“…[13] (and Refs. [2][3][4][5][6][7][10][11][12][13][14][15][16][17] and references therein), one can see that our results provide novel stability conditions to (4.17).…”

“…Now we state the following basic lemma (see Lemma 3.1 in Ref. [11] for 0 < q 1 which is an extension of Lemma 3.1 in Ref. [15] for q = 1 and cf.…”

Global stability for nonlinear dynamic equations with variable coefficients

“…Because the foundational lemmas from the discrete case proven by Muroya, Ishiwata, and Guglielmi [10] have all been generalized to arbitrary time scales in the previous section and in the remark above, the statements and proofs of the following theorems are very similar to those found in the discrete case in [10].…”

“…This sketch is motivated by ideas from Muroya, Ishiwata, and Guglielmi [10]. Assume that the solution x of (1.1) is greater (less) than 0.…”

“…Eq. (1.1) is studied extensively by Muroya, Ishiwata, and Guglielmi [10] in the case when T = Z; indeed many of our techniques in this paper are motivated directly by those in [10]; please also see Tkachenko and…”