PROPER SOLUTIONS AND LIMIT BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-OROER SYSTEMS OF DIFFERENTIAL EQUATIONS

Applied Mathematics and Mechanics (English Edition) ›› 1985, Vol. 6 ›› Issue (11): 1113-1120.

PROPER SOLUTIONS AND LIMIT BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-OROER SYSTEMS OF DIFFERENTIAL EQUATIONS

梁中超, 陈绍著

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

收稿日期:1984-07-09 出版日期:1985-11-18 发布日期:1985-11-18

PROPER SOLUTIONS AND LIMIT BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-OROER SYSTEMS OF DIFFERENTIAL EQUATIONS

Liang Zbong-chao, Chen Shao-zhu

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

Received:1984-07-09 Online:1985-11-18 Published:1985-11-18

摘要/Abstract

摘要： For the system of differential equations x=r(t)y,y=-a(t)f(x)g(y) where a(t)>0, r(t)>0 for t≥t; 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≥t_g. Several examples are given to illustrate the conditions of these results.

关键词: chaos, subharmonic bifurcation, heteroclinic orbit, periodic orbit

Abstract: For the system of differential equations x=r(t)y,y=-a(t)f(x)g(y) where a(t)>0, r(t)>0 for t≥t; 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≥t_g. Several examples are given to illustrate the conditions of these results.

Key words: chaos, subharmonic bifurcation, heteroclinic orbit, periodic orbit

梁中超;陈绍著. PROPER SOLUTIONS AND LIMIT BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-OROER SYSTEMS OF DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1985, 6(11): 1113-1120.

Liang Zbong-chao;Chen Shao-zhu. PROPER SOLUTIONS AND LIMIT BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-OROER SYSTEMS OF DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1985, 6(11): 1113-1120.

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PROPER SOLUTIONS AND LIMIT BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-OROER SYSTEMS OF DIFFERENTIAL EQUATIONS

PROPER SOLUTIONS AND LIMIT BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-OROER SYSTEMS OF DIFFERENTIAL EQUATIONS

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