The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations

Abstract

ABSTRACT. We investigate the boundary growth of positive superharmonic functions u on a bounded domain Ω in R n , n ≥ 3, satisfying the nonlinear elliptic inequalitywhere c > 0, α ≥ 0 and p > 0 are constants, and δ Ω (x) is the distance from x to the boundary of Ω. The result is applied to show the Harnack inequality for such superharmonic functions. Also, we study the existence of positive solutions, with singularity on the boundary, of the nonlinear elliptic equationwhere V and f are Borel measurable functions conditioned by the generalized Kato class.

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

“…Also, we obtain the following proposition, using a technique in our previous paper [8]. Proof Without loss of generality, we may assume that R = 1 and D ⊂ .…”