Boundary value problem for the four-dimensional Gellerstedt equation

Abstract

In this work, the solvability of the problem with Neumann and Dirichlet boundary conditions for the Gellerstedt equation in four variables was investigated. The energy integral method was used to prove the uniqueness of the solution to the problem. In addition to it, formulas for differentiation, autotransformation, and decomposition of hypergeometric functions were applied. The solution was obtained explicitly and expressed by Lauricella’s hypergeometric function.