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

Liang Zhong-chao; Chen Shao-zhu

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(11): 1027-1034

Liang Zhong-chao, Chen Shao-zhu. Proper Solutions and Limit Boundary Value Problems of Nonlinear Second-Order Systems of Differential Equations[J]. Applied Mathematics and Mechanics, 1985, 6(11): 1027-1034.

Citation:

PDF( 445 KB)

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

Liang Zhong-chao¹,
Chen Shao-zhu²

1.
Shandong Oceanography College, Qingdao;
2.
Shandong University, Jinan

Received Date: 1984-07-09
Publish Date: 1985-11-15

Abstract

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.

FullText(HTML)

References(2)

References

[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.