SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

doi:10.1016/S0252-9602(12)60186-6

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (6): 2377-2387.doi: 10.1016/S0252-9602(12)60186-6

SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

杨芬

College of Science, Wuhan University of Science and Technology, Wuhan 430081, China

收稿日期:2011-01-20 修回日期:2011-12-26 出版日期:2012-11-20 发布日期:2012-11-20
基金资助:
Supported by the Natural Science Foundation of China (10901126).

SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

YANG Fen

College of Science, Wuhan University of Science and Technology, Wuhan 430081, China

Received:2011-01-20 Revised:2011-12-26 Online:2012-11-20 Published:2012-11-20
Supported by:
Supported by the Natural Science Foundation of China (10901126).

摘要/Abstract

摘要：

The existence and uniqueness of singular solutions decaying like r^−m (see (1.4)) of the equation
Δu +∑^k_Xi=c_i|x|^l_iu^p_i = 0, x ∈ Rⁿ(0.1)
are obtained, where n ≥ 3, c_i> 0, l_i > −2, i = 1, 2, · · · , k, p_i > 1, i = 1, 2, · · · , k and the separation structure of singular solutions decaying like r⁻⁽ⁿ⁻²⁾ of eq. (0.1) are discussed. moreover, we obtain the explicit critical exponent p_s(l) (see (1.9)).

关键词: singular solution, decay, separation property, semilinear elliptic equation

Abstract:

Key words: singular solution, decay, separation property, semilinear elliptic equation

中图分类号:

35J60

杨芬. SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION[J]. 数学物理学报(英文版), 2012, 32(6): 2377-2387.

YANG Fen. SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION[J]. Acta mathematica scientia,Series B, 2012, 32(6): 2377-2387.

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SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

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