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2018 Asymptotic behavior of positive solutions of the Henon equation
Biao Wang, Zhengce Zhang
Rocky Mountain J. Math. 48(8): 2717-2749 (2018). DOI: 10.1216/RMJ-2018-48-8-2717

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.

Citation

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Biao Wang. Zhengce Zhang. "Asymptotic behavior of positive solutions of the Henon equation." Rocky Mountain J. Math. 48 (8) 2717 - 2749, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2717

Information

Published: 2018
First available in Project Euclid: 30 December 2018

zbMATH: 06999282
MathSciNet: MR3895001
Digital Object Identifier: 10.1216/RMJ-2018-48-8-2717

Subjects:
Primary: 35B09, 35C20, 35J61

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 8 • 2018
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