CLASSIFICATION AND EXISTENCE OF POSITIVE SOLUTIONS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAY DEPENDING ON THE UNKNOWN FUNCTION

A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/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 obtained.

一类三阶拟线性微分方程非振动解的存在性

讨论三阶拟线性微分方程(p(t)∣u″∣α-1u″)′+q(t)∣u∣β-1u=0非振动解的存在性.其中α>0,β>0,p(t)和q(t)是定义在区间[a,∞)上的连续函数,且满足当t≥a时p(t)>0,q(t)>0.给出了当t→∞时此方程满足∫∞(p(t1))1/αdt=∞的特殊非振动解存在的充分必要条件.

一类非线性常微分方程正解的存在性与渐进性

本文讨论了一类非线性二阶常微分方程 0)()()1())((1=-++xuxpxxum 0],1,0(>mx 正解的存在问题,用非线性算子方法证明了正解的存在性、唯一性。并且,给出了这个正解的一个逼近。推广了文献[1]的某些结论。

一类三阶非线性微分方程最终正解的存在性

利用Schauder-Tychonoff不动点定理讨论了一类三阶非线性微分方程在特殊条件下的最终正解存在的充分必要条件.

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)

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 .

一类三阶微分方程特殊正解的存在性

利用Schauder-Tychonoff不动点定理和分析技巧,研究了一类三阶非线性微分方程正解中最大解和最小解存在的充分和必要条件,并讨论了方程解的渐近性.

时滞依赖于未知函数的高阶非线性微分方程正解的分类及存在性(英文)

研究了一类时滞依赖于未知函数的高阶非线性微分方程(an-1(t)(an-2(t)…(a1(t)(x(t))x′(t))′…)′)′+f(t,x(t),x(Δ(t,x(t))))=0.其中∫0∞aid(ss)<∞(i=1,2,…,n-1),n≥2为偶数.根据最终正解的渐近性给出了解的各种分类情况,并建立了存在这些解的充分和必要条件.

CONVERGENT AND DIVERGENT SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR DIFFERENCE SYSTEM

In this paper, we are concerned with the existence of convergent or divergent solutions of two-dimensional nonlinear difference system of the form{xn＋1=αnxn＋bnf（yn）,yn=cnyn-1＋dng（xn）.We＇ classify their solutions according to asymptotic behavior and give some sufficient and necessary conditions for the existence of solutions of such classes by using the method of the fixed point theorem. We also give an example and show how the results can be applied to certain difference systems.

一类三阶拟线性微分方程非振动解的渐近性

主要讨论的是一类三阶拟线性微分方程(p(t)|u″|^(α-1)u″)′+q(t)|u|^(β-1)u=0其中α>0,β>0,p(t)和q(t)是定义在区间[a,∞)上的连续函数,且满足当t≥a时p(t)>0,q(t)>0.当t→∞时此方程满足∫_a~∞1/((p(t))^(1/α))dt=∞的特殊非振动解存在的充分必要条件.