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

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 , p>1, λ>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.