Global attractivity for a nonlinear difference equation with variable delay

Matsunaga, Hideaki; Hara, Tadayuki; Sakata, Sadahisa

doi:10.1016/s0898-1221(00)00297-2

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Introduction4

R (T)u (T) = F (T U(t + 1) U(t) U(t − 1)) T ∈ R1

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Cited by 61 publications

(32 citation statements)

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“…For the general background of difference equations, one can refer to the monographs [1,2,3]. For the past twenty years, there has been much progress on the qualitative properties of difference equations, which included result in stability and attractive [13,15] and result in oscillation and other topics, see [1,2,3,8,9,10,12,21,22,23,24,25]. Therefore, it is worthwhile to explore this topic.…”

Section: Introductionmentioning

confidence: 99%

Existence of periodic solutions for second-order nonlinear difference equations

Ren¹,

Li²,

Shi³

2016

J. Nonlinear Sci. Appl.

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By using the critical point method, the existence of periodic solutions for second-order nonlinear difference equations is obtained. The proof is based on the Saddle Point Theorem in combination with variational technique. The problem is to solve the existence of periodic solutions of second-order nonlinear difference equations. One of our results obtained complements the result in the literature.

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Section: Introductionmentioning

confidence: 99%

Existence of periodic solutions for second-order nonlinear difference equations

Ren¹,

Li²,

Shi³

2016

J. Nonlinear Sci. Appl.

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“…The global stability of various partial classes of Eqs. (1) was studied in [1][2][3][4][5][6][7][8][9][10][11]. We define a functional M : R k+1 → R + as follows: M(φ) = max i {0, φ i }.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On the Global Stability of One Nonlinear Difference Equation

2004

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“…For the general background of difference equations, one can refer to monographs [1,21,25]. Since the last decade, there has been much progress on the qualitative properties of difference equations, which included results on stability and attractivity [13,23,39] and results on oscillation and other topics, see [1][2][3]5,10,[16][17][18][19]22,[34][35][36][37][38].…”

Section: R (T)u (T) = F (T U(t + 1) U(t) U(t − 1)) T ∈ Rmentioning

confidence: 99%