On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance
نویسندگان
چکیده
منابع مشابه
The Generalized Emden-Fowler Equation
We give the description of nonlinear nonautonomous ordinary differential equations of order n with a so-called reducible linear part. The group classification of generalized Emden-Fowler equations of the mentioned class is done. We have found such laws of the variation of f(x) that the equation admits one, two, or tree one-parameter Lie groups.
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We consider the following anisotropic Emden-Fowler equation ∇(a(x)∇u) + εa(x)e = 0 in Ω, u = 0 on ∂Ω where Ω ⊂ R is a bounded smooth domain and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of bubbling solutions. We show that at given local maximum points of a(x), there exists arbitrarily many bubbles. As a consequence, the quanti...
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ژورنال
عنوان ژورنال: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
سال: 1991
ISSN: 0334-2700,1839-4078
DOI: 10.1017/s0334270000008535