A generalization of the Lane–Emden equation

Abstract We consider a class of second-order initial-value problems, which includes the well-known Lane–Emden equation from astrophysics as a special case. Local existence, global existence and uniqueness of solutions are proven.

[1]  C. Mohan,et al.  Power-series solutions of the Lane-Emden equation , 1980 .

[2]  Patrick Habets,et al.  Upper and Lower Solutions for a Generalized Emden-Fowler Equation , 1994 .

[3]  P. Ranganathan.  Solutions of some classes of second order non-linear ordinary differential equations , 1988 .

[4]  O. Bhutani,et al.  On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance , 1991, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[5]  Concavity and monotonicity properties of solutions of Emden-Fowler equations , 1988 .

[6]  F. Rothe.  A variant of frobeniu' method for the emden fowler equation , 1997 .

[7]  S. Hastings.  Boundary value problems in one differential equation with a discontinuity , 1965 .

[8]  A non-elliptic solution of the Lane-Emden equation for index n=5 , 1977 .

[9]  B. K. Datta.  RETRACTED ARTICLE: Analytic solution to the Lane-Emden equation , 1996 .

[10]  N. Shawagfeh.  Nonperturbative approximate solution for Lane–Emden equation , 1993 .

[11]  P. Leach.  First integrals for the modified Emden equation q̈+α(t) q̇+qn =0 , 1985 .

[12]  P. Rosenau.  A note on integration of the Emden-Fowler equation , 1984 .

[13]  G. Horedt.  Topology of the Lane-Emden equation , 1987 .

[14]  M. Beech.  An approximate solution for the polytropen=3 , 1987 .

[15]  P. Ranganathan.  Integrals of the Emden-Fowler equations , 1992 .

[16]  W. Mydlarczyk.  A singular initial value problem for second and third order differential equations , 1995 .

[17]  J. Myjak,et al.  A generalized Emden-Fowler equation with a negative exponent , 1994 .