SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

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

Abstract

Abstract:

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)).

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

CLC Number:

35J60

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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