Abstract
ABSTRACTWe consider the generalized Gellerstedt equation in a domain . Here m,n,k,l>0 are constants. The goal of the present paper is finding the fundamental solutions for the generalized four-dimensional Gellerstedt equation in an explicit form. Solutions are expressed by Lauricella hypergeometric functions of four variables. By means of expansion of the hypergeometric Lauricella function by products of Gauss hypergeometric functions, it is proved that the found solutions have a singularity of the order at . These fundamental solutions are important for solving a number of boundary value problems for the aforementioned degenerate elliptic equation. In addition, some properties of these solutions are shown.
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