MINIMAL POSITIVE ENTIRE SOLUTION OF SEMILINEAR ELLIPTIC EQUATION

摘要

In this paper, the singular semilinear elliptic equation Δu + q(x)u~α + p(x)u~(-β) - h(x)u~γ = 0, x ∈ R~N, N ≥ 3, is studied via the super and sub-solution method, where Δ is the Laplacian operator, α ∈ [0,1), β > 0, and γ ≥ 1 are constants. Under a set of suitable assumptions on functions q(x), p(x) and h(x), it is proved that there exists for the equation one and only one minimal positive entire solution.