本刊英文版2009年52卷第9期摘要

The fundamental solution of the Keldysh type operator
CHEN ShuXing
Abstract In this paper we discuss the fundamental solution of the Keldysh type operator Lαu =△ δ^2u/δx^2＋yδ^2u/δy^2＋αδu/δy, which is a basic mixed type operator different from the Tricomi operator. The is obtained. It is shown that the fundamental solution of the Keldysh type operator with a 〉-1/2 fundamental solution for such an operator generally has stronger singularity than that for the Tricomi has to be operator. Particularly, the fundamental solution of the Keldysh type operator with a 〈1/2 defined by using the finite part of divergent integrals in the theory of distributions.
Keywords： mixed type equation, Keldysh operator, fundamental solution, finite part of divergent integral