摘要
本文讨论了一类滞后型泛函微分方程解的渐近性态。其中一些结果包含了Haddock等在[3]中利用不变性原理讨论方程解的性态所得某些结果,如他们的例3、4就是本文推论1的特例。
Consider the RFDE x'(t)=F(x(t))-G(x(t-t_1(t)),…,x(t-τ_n(t))) (1) where F∈C(R, R) is not increasing for u∈R.0≤τ_i(t)≤r, and there is a T_i>t_0 for At_0∈R snch that t-τ_i(t)≤t_0 for t∈[t_0,T_i]. (i=1,2,…,n). G∈C(R^n, R) and G(x_1,…,x_(i-1),x_i,x_(i+1),…,x_n)≥G(x_1,…,x_(i-1),x_i,x_(i+1),…,x_n) for any (x_,…,x_(i-1)x_i, x_(i+1),…,x_n), (x_1,…,x_(i-1)x_i,…,x_n)∈R^n, where x_i>_i. we have the following results. Thereom2. If there exists a constant a such that (ⅰ) F(x)<G(x,x,…,x)≤F(α) for x∈(α,+∞) (ⅱ) F(x)>G(x,x,<,x)≥F(α) for x∈(-∞,α) Then x(σ,φ)(t)=α, where x(σ,φ)(t) is the solution with the initial condition(σ,φ)∈ R×C. of RFDE (1). Corollary2 Consider the equation x'(t)=-Ax~β(t)+sum from i=1 to n α_ix~β(t-τ_i (t)). where α_i≥0(i=1,2,,…,n) and β is the ratio of two odd numbers. If A=sum from i=1 to n α_i, then any solution of the equation tends to a fiuite constant as t→+∞; If A>sum from i=1 to n α_i, then any solution of the equation tends to zero as t→+∞.
出处
《东北师大学报（自然科学版）》
CAS
CSCD
1990年第4期13-19,共7页
Journal of Northeast Normal University(Natural Science Edition)
基金
国家自然科学基金
