Singular Positive Radial Solutions for a General Semilinear Elliptic Equation

The existence and uniqueness of singular solutions decaying like r−m (see (1.4)) of the equation equation(0.1)Δu+∑i=1kci|x|liupi=0,         x∈ℝn 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)).