Proper solutions and limit boundary value problems of nonlinear second-order systems of differential equations |
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Authors: | Liang Zhong-chao Chen Shao-zhu |
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Institution: | 1. Shandong Oceanography College, Qingdao;2. Shandong University, Jinan |
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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≥tg. Several examples are given to illustrate the conditions of these results. |
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