Square-summable stability in parabolic Volterra difference equations

Shi, Bao; Wang, Z. C.; Yu, Jiaju

doi:10.4310/maa.1996.v3.n2.a7

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Theorem 13 Assume That For Any Sequence Of Disjoint Subsets1

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Cited by 6 publications

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“…One may see Shi [5,6] and Shi, Wang and Yu [7][8][9][10] for the studies on Volterra reaction-diffusion difference equations of neutral type.…”

Section: Theorem 13 Assume That For Any Sequence Of Disjoint Subsetsmentioning

confidence: 99%

Asymptotic behavior for non-oscillatory solutions of difference equations with several delays in the neutral term

Shi

Zeng

2008

J. Appl. Math. Comput.

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In this paper, we first consider difference equations with several delays in the neutral term of the form ⎛study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution of ( * ) under some hypotheses. Moreover, we consider reaction-diffusion difference equations with several delays in the neutral term of the formr j u n−ρ j ,m ⎞ ⎠ + q n,m u n−τ,m = a 2 2 2 u n+1,m−1 for (n, m) ∈ Z + (0) × , study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution under some hypotheses.

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“…One may see Shi [5,6] and Shi, Wang and Yu [7][8][9][10] for the studies on Volterra reaction-diffusion difference equations of neutral type.…”

Section: Theorem 13 Assume That For Any Sequence Of Disjoint Subsetsmentioning

confidence: 99%

Asymptotic behavior for non-oscillatory solutions of difference equations with several delays in the neutral term

Shi

Zeng

2008

J. Appl. Math. Comput.

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show abstract

On a Delay Reaction-Diffusion Difference Equation of Neutral Type

Shi

2002

Acta Math Sinica

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Asymptotic constancy of solutions of linear parabolic Volterra difference equations

Shi

Wang

1996

Computers & Mathematics with Applications

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Square-summable stability in parabolic Volterra difference equations

Abstract: ABSTRACT. We consider some linear and nonlinear parabolic Volterra difference equations of the formsfor 771 = 0,1,..., M-1 and n = 0,1,..., and we obtain several sufficient conditions for the square-summable stability and ^-square-summable stability of the zero solution.

Cited by 6 publications

References 10 publications

Asymptotic behavior for non-oscillatory solutions of difference equations with several delays in the neutral term

Asymptotic behavior for non-oscillatory solutions of difference equations with several delays in the neutral term

On a Delay Reaction-Diffusion Difference Equation of Neutral Type

Asymptotic constancy of solutions of linear parabolic Volterra difference equations

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