In this paper, a sufficient condition for boundedness and persistence of the solutions of the following delay difference equation is obtained. A conjecture by G.Ladas is proved herexn+1=A/xpn+B/xqn-1,\ n=0,1,…q, x-1,...In this paper, a sufficient condition for boundedness and persistence of the solutions of the following delay difference equation is obtained. A conjecture by G.Ladas is proved herexn+1=A/xpn+B/xqn-1,\ n=0,1,…q, x-1, x0∈(0,∞). Received June 2,1997. Revised September 15, 1997.1991 MR Subject Classification:39A10.展开更多
Consider the neutral delay difference equation △[p(t)x(t)-q(t)x(t-τ)] + r(t)x(t-δ(t)) =0 (*)where t ∈{a, a + 1, a + 2,…} and p(t) > 0, q(t) ≥ 0, r(t) ≥ 0, δ(t) ∈ {0, 1, 2,…} with,lim(t-δ(t)) =∞ and τ∈...Consider the neutral delay difference equation △[p(t)x(t)-q(t)x(t-τ)] + r(t)x(t-δ(t)) =0 (*)where t ∈{a, a + 1, a + 2,…} and p(t) > 0, q(t) ≥ 0, r(t) ≥ 0, δ(t) ∈ {0, 1, 2,…} with,lim(t-δ(t)) =∞ and τ∈ { 1, 2, 3,…}. Note that the delay of the difference equation may vary, thus the equation may not be of constant order. We obtain some sufficient conditions for the oscillation of Equation (*) and the second order self-adjoint difference equation △[p(t-1)△y(t-1)]+r(t)y(t) = 0.And the work in Timothy Peil [5] is improved.AMS (1991) No. 39A10, 39A12展开更多
Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to...Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.展开更多
文摘In this paper, a sufficient condition for boundedness and persistence of the solutions of the following delay difference equation is obtained. A conjecture by G.Ladas is proved herexn+1=A/xpn+B/xqn-1,\ n=0,1,…q, x-1, x0∈(0,∞). Received June 2,1997. Revised September 15, 1997.1991 MR Subject Classification:39A10.
文摘Consider the neutral delay difference equation △[p(t)x(t)-q(t)x(t-τ)] + r(t)x(t-δ(t)) =0 (*)where t ∈{a, a + 1, a + 2,…} and p(t) > 0, q(t) ≥ 0, r(t) ≥ 0, δ(t) ∈ {0, 1, 2,…} with,lim(t-δ(t)) =∞ and τ∈ { 1, 2, 3,…}. Note that the delay of the difference equation may vary, thus the equation may not be of constant order. We obtain some sufficient conditions for the oscillation of Equation (*) and the second order self-adjoint difference equation △[p(t-1)△y(t-1)]+r(t)y(t) = 0.And the work in Timothy Peil [5] is improved.AMS (1991) No. 39A10, 39A12
基金Supported by the Science Foundation of Educational Committee of Hunan Province
文摘Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.
