Limits at Infinity of Superharmonic Functions and Solutions of Semilinear Elliptic Equations of Matukuma Type

In an unbounded domain Ω in ℝ ⁿ (n ≥ 2) with a compact boundary or Ω = ℝ ⁿ , we investigate the existence of limits at infinity of positive superharmonic functions u on Ω satisfying a nonlinear inequality like as where Δ is the Laplacian and c > 0 and p > 0 are constants. The result is applicable to positive solutions of semilinear elliptic equations of Matukuma type. This work was partially supported by Grant-in-Aid for Young Scientists (B) (No. 19740062), Japan Society for the Promotion of Science.