Abstract
For the system of differential equations (fx1113-1) 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.
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References
Liang Zhong-chao, The boundary value probelm on an infinite interval for nonlinear differential equation of second order (Chinese, English summary), Acta Math. Appl., Sinica, 4 (1981), 272–279, MR83c: 34021.
Taliaferro S., On the positive solutions of (ie1120-2) Nonlinear Analysis, 2 (1978), 437–446.
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Communicated by Li Li
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Zhong-chao, L., Shao-zhu, C. Proper solutions and limit boundary value problems of nonlinear second-order systems of differential equations. Applied Mathematics and Mechanics 6, 1113–1120 (1985). https://doi.org/10.1007/BF03250510
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DOI: https://doi.org/10.1007/BF03250510