Acta mathematica scientia, Series B >
SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION
Received date: 2011-01-20
Revised date: 2011-12-26
Online published: 2012-11-20
Supported by
Supported by the Natural Science Foundation of China (10901126).
The existence and uniqueness of singular solutions decaying like r−m (see (1.4)) of the equation
Δu +∑kXi=ci|x|liupi = 0, x ∈ Rn (0.1)
are obtained, where n ≥ 3, ci > 0, li > −2, i = 1, 2, · · · , k, pi > 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 ps(l) (see (1.9)).
YANG Fen . SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION[J]. Acta mathematica scientia, Series B, 2012 , 32(6) : 2377 -2387 . DOI: 10.1016/S0252-9602(12)60186-6
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