SOLUTION OF GENERALIZED EMDEN-FOWLER EQUATIONS WITH 2 SYMMETRIES

被引：30
|
作者：
MELLIN, CM
MAHOMED, FM
LEACH, PGL
机构：
[1] UNIV WITWATERSRAND,CTR NONLINEAR STUDIES,JOHANNESBURG 2001,SOUTH AFRICA
[2] UNIV NATAL,DEPT MATH & APPL MATH,DURBAN 4001,SOUTH AFRICA
来源：
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 1994年 / 29卷 / 04期
关键词：
D O I：
10.1016/0020-7462(94)90021-3
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The generalized Emden-Fowler equation y'' + p(x)y' + r(x)y = f(x)y'' has a single point symmetry under a certain constraint on f(x). Although the order of the equation can be reduced by one, integration of the resulting Abel's equation of the second kind in closed form is not generally possible. Under a stronger constraint there exist two symmetries G1 and G2, such that [G1, G2] = (cst)G2 and reduction to quadratures becomes trivial. The special cases n = 2 and n = - 3 are treated in detail.
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页码：529 / 538
页数：10
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