The radial positive solutions of the Matukuma equation in higher dimensional space: Singular solution

[摘要] The work is an extensive study of the M-solutions (singular at r = 0) which is one of the three different types of radial positive solutions of the general Matukuma equation 1/r(N-1) (r(N-1) phi')' = - r(lambda-2)/(1+r(2))(lambda/2) phi(p) > 1, lambda > 0, N > 3. We apply an asymptotic expansion method which begins with rough estimate and improves the accuracy step by step to the desired extend. Comparing with the case when N = 3 (see Batt and Li, 2010 [5]), such asymptotic expansions require more delicate study. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Matukuma equation;Vlasov-Poisson system;Radial solutions;Singular solution