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1

Bifurcation in a nonlinear steady state system

Wang G. Q., Cheng S. S.

Opuscula Mathematica

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2010

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Vol. 30, no. 3

349-360

EN

The steady state solutions of a nonlinear digital cellular neural network with ω neural units and a nonnegative variable parameter λ are sought. We show that λ = 1 is a critical value such that the qualitative behavior of our network changes. More specifically, when ω is odd, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ ∈ [1, ∞), steady states cannot exist; while when ω is even, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ = 1, there are no nontrivial steady states, and for λ ∈ (1, ∞), there are two fully oscillatory steady states. Furthermore, the number of existing nontrivial solutions cannot be improved. It is hoped that our results are of interest to digital neural network designers.

2

Oscillations of a higher order nonlinear differential equations with impulses

Wen -wen K., Wang G. Q., Cheng S. S.

Demonstratio Mathematica

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2010

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Vol. 43, nr 3

575-603

EN

Impulsive differential equations are important in simulation of processes with jump conditions. Although there are quite a few studies on the oscillation properties of low order equations, there are not too many studies of higher order equations. In this paper, we derive several oscillation criteria which are either new or improve several recent results in the literature. In addition, we provide several examples to illustrate the use of our results.

3

Asymptotic stability of a neutral integro-differential equation

Wang G., Cheng S. S.

Opuscula Mathematica

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2006

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Vol. 26, no. 3

515-527

EN

The global stability behavior of a non-autonomous neutral functional integro-differential equation is studied. A sufficient condition for every solution of this equation to tend to zero is given.

4

On two second order half-linear difference equations

Zhang G., Cheng S. S.

Fasciculi Mathematici

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2005

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Nr 35

163-175

EN

In this paper, two second order half-linear difference equations are considered. By establishing their connections with a standard half-linear difference equation, we are able to obtain sufficient conditions for existence and nonexistence of eventually positive solutions.

5

Periodic solutions of two-species difusion models with continuous time delays

Huo H.-F., Li W.-T., Cheng S. S.

Demonstratio Mathematica

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2002

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Vol. 35, nr 2

433-446

EN

Two-species prey-predator diffusion models with periodic coefficients and continuous time delays are investigated. We derive sufficient conditions that guarantee the existence of positive periodic solutions which are globally asymptotically stable.

6

A multivariate oscillation theorem

Cheng S. S., Liu S. T., Zhang G.

Fasciculi Mathematici

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1999

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Nr 30

15-22

EN

An oscillation criterion is derived for a multivarjate partial difference equation.

7

Nonexistence criteria for positive solutions of a discrete elliptic equation

Cheng S. S., Zhang B.-G.

Fasciculi Mathematici

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1998

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Nr 28

19-30

EN

A nonlinear elliptic type partial difference equation with a forcing terrn is studied in this paper. By means of an averaging technique, the problem of non-existence of positive solutions is reduced to that of forced recurrence relations. Several sample non-existence criteria are given for these recurrence relations which in turn yield non-existence criteria for the discrete elliptic equation.