Abstract

In this paper the method of moving spheres is used to derive a Harnack-type inequality for positive solutions of

where n ≥ 4, ℝ₊ⁿ is the upper half of Euclidean space and B₁⁺ is the upper half unit ball. Under suitable assumptions on K(x) and c(x), we show that there is a positive constant C such that for all positive solutions u, a Harnack-type inequality holds. As a consequence of this inequality we obtain the following energy estimate