ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF THE HENON EQUATION

被引：1

作者：

Wang, Biao ^{[1
]}

Zhang, Zhengce ^{[2
]}

机构：

[1] Xian Univ Sci & Technol, Coll Sci, Xian 710054, Shaanxi, Peoples R China

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2018年 / 48卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Henon equation; singular solutions; asymptotic expansions; SEMILINEAR ELLIPTIC-EQUATIONS; RADIAL SYMMETRY; STEADY-STATES; CLASSIFICATION; UNIQUENESS; STABILITY; RN;

D O I：

10.1216/RMJ-2018-48-8-2717

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 [2, 9], our results are more accurate.

引用

页码：2717 / 2749

页数：33

共 28 条

[1] ON THE RADIUS CONTINUITY OF THE MODELS OF POLYTROPIC GAS SPHERES WHICH CORRESPOND TO THE POSITIVE SOLUTIONS OF THE GENERALIZED EMDEN-FOWLER EQUATION [J].

BATT, J ;

PFAFFELMOSER, K .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1988, 10 (05) :499-516

[2] The Positive Solutions of the Matukuma Equation and the Problem of Finite Radius and Finite Mass [J].

Batt, Juergen ;

Li, Yi .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 198 (02) :613-675

[3]

Bellman R., 1953, STABILITY THEORY DIF

[4] NONLINEAR ELLIPTIC-EQUATIONS ON COMPACT RIEMANNIAN-MANIFOLDS AND ASYMPTOTICS OF EMDEN EQUATIONS [J].

BIDAUTVERON, MF ;

VERON, L .

INVENTIONES MATHEMATICAE, 1991, 106 (03) :489-539

[5] Finite Morse index solutions of an elliptic equation with supercritical exponent [J].

Dancer, E. N. ;

Du, Yihong ;

Guo, Zongming .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (08) :3281-3310

[6] On the stability of the positive radial steady states for a semilinear Cauchy problem [J].

Deng, YB ;

Li, Y ;

Liu, Y .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 54 (02) :291-318

[7] On the stability of the positive steady states for a nonhomogeneous semilinear Cauchy problem [J].

Deng, Yinbin ;

Li, Yi ;

Yang, Fen .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 228 (02) :507-529

[8] On the classification of solutions of the Lane-Emden equation on unbounded domains of RN [J].

Farina, Alberto .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (05) :537-561

[9] GLOBAL AND LOCAL BEHAVIOR OF POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS [J].

GIDAS, B ;

SPRUCK, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1981, 34 (04) :525-598

[10]

Hassard BD., 1981, Theory and Applications of Hopf Bifurcation, V41

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