二阶非线性微分方程组的正规解及极限边值问题

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Proper Solutions and Limit Boundary Value Problems of Nonlinear Second-Order Systems of Differential Equations

摘要: 本文对微分方程组其中a(t)>0,r(t)>0,t≥t₀;f(x)对x>0正值递减;g(y)>0,给出存在正规解,有界正规解或两类无穷区间[c,∞)(c≥t₀)上边值问题解的充要条件.同时给出若干例子说明结果的条件.

Abstract: For the system of differential equations , where a(t)>0, r(t)>0 for t≥t₀, f(x) >0 and is decreasing for x>0 g(y)>0, we give necessary and sufficient condition of the existence of a proper solution, a bounded proper solution or solutions of two kinds of boundary value problems on an infinite interval [c,∞] c≥t₀. Several examples are given to illustrate the conditions of these results.

[1]	梁中超,二阶非线性微分方程在无穷区间上的边值问题,应用数学学报,4 (1981), 272-279.
[2]	Taliaferro S On the positive solutions of y''+φ(t)y^-λ=0,Nonlinear Analysis,2(1978),437-446.