Solvability of a certain integral equation and its application

Abstract

where Q is a sufficiently small region in Rn+ and h(x,y) is a given kernal function belonging to the class Kα,βγ(Rn+,Rn+) defined in §1. In order to solve (0,1), we shall make use of the Neumann series and verify its absolute convergence for a sufficiently small Q Secondly, as its application, we shall construct a fundamental solution for the degenerated elliptic operator which was already treated in author's paper [3]. More precisely, in [3] we treated the operator A defined on a domain Ω in Rn which is approximated, near the boundary, by the following simple operator Lα in the half space Rn+: