一类无穷时滞泛函微分方程解的渐近性态

The asymptotic behavior of solutions to a class of functional differential equations with infinite delay

研究一类无穷时滞泛函微分方程 x(t) =f(xt)解的渐近性态。当f为合作映射时 ,得到了解半流的单调性和解的单调性 ,给出了有界解的ω-极限集的结构 ,在一定的条件下证明了正平衡态的唯一性和解的收敛性 。

This paper is concerned with the asymptotic behavior of solutions to a class of functional differential equations with infinite delay. Under the assumption that the mapping of right-side of the equations is cooperative, the monotonicity of solution semiflows as well as solutions,and the structure of ω-limit set for bounded solutions are obtained. The uniqueness of positive equilibria and convergence of solutions are also gained under the additive assumptions. an example is contained to explain the main results in this paper.