In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y_n+py_(n-k))+q_ny_(n-)=0 for n∈Z^+(0) (1*) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994,...In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y_n+py_(n-k))+q_ny_(n-)=0 for n∈Z^+(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-oscillatory solution of (1~*) with p=1 tends to zero as n→∞ Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form: Δ_1(u_(n,m)+pu_(n-k,m)+q_(n,m)u_(n-m)=a^2Δ_2~2u_(n+1,m-1) for (n,m)∈Z^+(0)×Ω. (2*) study various casks of p in the neutral term and obtain that if p≥-1 then every non-oscillatory solution of (2~*) tends uniformly in m∈Ω to zero as n→∞: if p=-1 then every solution of (2~*) oscillates 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.展开更多
基金Research supported by Youth Science Foundation of Naval Aeronautical Engineering AcademyNational Natural Science Foundation of China (# 69974032).
文摘In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y_n+py_(n-k))+q_ny_(n-)=0 for n∈Z^+(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-oscillatory solution of (1~*) with p=1 tends to zero as n→∞ Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form: Δ_1(u_(n,m)+pu_(n-k,m)+q_(n,m)u_(n-m)=a^2Δ_2~2u_(n+1,m-1) for (n,m)∈Z^+(0)×Ω. (2*) study various casks of p in the neutral term and obtain that if p≥-1 then every non-oscillatory solution of (2~*) tends uniformly in m∈Ω to zero as n→∞: if p=-1 then every solution of (2~*) oscillates 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.
