scholarly journals The Lane-Emden equation and its generalizations

Astrophysics ◽  
10.5772/33136 ◽  
2012 ◽  
Author(s):  
Chaudry Khalique
Keyword(s):  
Emden Equation

Fast and Slow Decaying Solutions of Lane–Emden Equations Involving Nonhomogeneous Potential

2020 ◽  
Vol 20 (2) ◽  
pp. 339-359
Author(s):  
Huyuan Chen ◽  
Xia Huang ◽  
Feng Zhou
Keyword(s):  
Positive Solutions ◽  
Emden Equation

AbstractOur purpose in this paper is to study positive solutions of the Lane–Emden equation-\Delta u=Vu^{p}\quad\text{in }\mathbb{R}^{N}\setminus\{0\},perturbed by a nonhomogeneous potential V, with p\in(\frac{N}{N-2},p_{c}), where {p_{c}} is the Joseph–Ludgren exponent. We construct a sequence of fast and slow decaying solutions with appropriated restrictions for V.

A New Solution of the Lane-Emden Equation of Index n=5.

1962 ◽  
Vol 136 ◽  
pp. 680 ◽  
Author(s):  
Shambhunath Srivastava
Keyword(s):  
Emden Equation

Solutions of a generalized Emden equation and their physical significance

1990 ◽  
Vol 41 (8) ◽  
pp. 4166-4173 ◽  
Author(s):  
J. M. Dixon ◽  
J. A. Tuszyński
Keyword(s):  
Physical Significance ◽  
Emden Equation

scholarly journals On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance

1991 ◽  
Vol 32 (4) ◽  
pp. 457-468 ◽  
Author(s):  
O. P. Bhutani ◽  
K. Vijayakumar
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Lie Group ◽  
Variational Principles ◽  
First Integrals ◽  
Noether Theorem ◽  
Repeated Application ◽  
Scale Invariant ◽  
Emden Equation ◽  
Fowler Equation

AbstractAfter formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classical Emden equations. A comparative study with Bluman-Cole and scale-invariant techniques reveals quite a number of remarkable features of the techniques used here.

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