TITLE

On a Delay Reaction-Diffusion Difference Equation of Neutral Type

AUTHOR(S)
Shi, Bao
PUB. DATE
October 2002
SOURCE
Acta Mathematica Sinica;2002, Vol. 18 Issue 4, p755
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, we first consider a delay diffrence equation of neutral type of the form: Δ(y[SUBn]+py[SUBn-k]) + q[SUBn]y[SUBn-l] = 0 for n ∈ Z[SUP+](0) (1∗) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241-248) to guarantee that every non-oseillatory solution of (1∗) with p = 1 tends to zero as n → ∞. Moreover, we eonsider a delay reaction-diffusion difference equation of neutral type of the form: Δ[SUB1](u[SUBn,m] + pu[SUBn-k,m]) + q[SUBn,m] u[SUBn-l,m] = a[SUP2] Δ[SUP2,SUB2]] u[SUBn+1,m-1] for (n, m) &isin Z[SUP+] (0) × Ω, (2∗) study various cases of p in the neutral terra and obtain that if p ≥ -1 then every non-oscillatory solution of (2∗) tends uniformly in ∈ Ω to zero as n → ∞; if p = -1 then every solution of (2∗) oseillates and if p < -1 then every non-oscillatory solution of (2∗) goes uniformly in m ∈ Ω to infinity or minus infinity as n → ∞ under some hypotheses.
ACCESSION #
7431804

 

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