Document Type

Article

Publication Date

11-2010

Abstract

This work is an extensive study of the 3 different types of positive solutions of the Matukuma equation 1r2(r2ϕ′)′=−rλ−2(1+r2)λ/2ϕp,p>1,λ>0 : the E-solutions (regular at r = 0), the M-solutions (singular at r = 0) and the F-solutions (whose existence begins away from r = 0). An essential tool is a transformation of the equation into a 2-dimensional asymptotically autonomous system, whose limit sets (by a theorem of H. R. Thieme) are the limit sets of Emden–Fowler systems, and serve as a characterization of the different solutions. The emphasis lies on the study of the M-solutions. The asymptotic expansions obtained make it possible to apply the results to the important question of stellar dynamics, solutions to which lead to galactic models (stationary

Comments

Article available for download is the author's version. The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-010-0315-9.