Asymptotic behavior of positive solutions of the Henon equation

Abstract

We investigate the radial positive solutions of the Henon equation. It is known that this equation has three different types of radial solutions: the M-solutions (singular at $r=0$), the E-solutions (regular at $r=0$) and the F-solutions (whose existence begins away from $r=0$). For the M-solutions and E-solutions, by virtue of some prior estimates, we adopt a circulating iterative method, step-by-step, to derive their precise asymptotic expansions. In particular, the M-solution has an extremely plentiful structure, and its asymptotic expansions are more complicated. In contrast to previous research Bratt and Pfaffelmoser, and Gidas and Spruck, our results are more accurate.