A remark on the generalization of Harnack's first theorem

Abstract

and under one of those uniqueness conditions, Harnack's first theorem was extended to the solution of the equation (1. 1). It was the case where the function f(x, u, p) was non-decreasing with respect to u. In the present paper, we consider the case where the function f(x, u, p) has not necessarily the above-mentioned property, and since Harnack's first theorem for solutions of the elliptic differential equation is really based on the continuous dependence of solutions upon the boundary data, we will here treat of this dependence. Regarding the notations used in the present paper, confer the above-cited papers.