具状态时滞的高阶非线性微分方程正解正在性及分类(英文)

Classification and Existence of Positive Solutions of Higher-order Nonlinear Differential Equations with State Dependent Delays

本文研究一类形如 (r(t)x(n- 1) (t) )′+f(t,x(t) ,x(Φ(t,x(t) ) ) =0 的具状态时滞的高阶非线性微分方程 .按照最终正解的量级给出了它们的分类及存在的充分条件 .

A class of higher-order nonlinear differential equations with state dependent delays of the from(r(t)x (n-1) (t))′+f(t, x(t), x(Φ(t, x(t))))=0in the case when ∫ ∞ 0ds/r(s)=∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also provided.