The Dirichlet Problem for an Elliptic Equation with Singular Coefficients in a Semi-Cylindrical Domain

Dirichlet-Neumann Spectral Problems for Three-Dimensional Elliptic Equations With Singular Coefficients

“…, n = 1, 3, 5, ..., 0, n = 2, 4, 6, ... . Consequently, function (32) satisfies the first condition (21). Now let us show that function (32) satisfies the second condition (21).…”

“…Many studies have been devoted to finding eigenvalues and eigenfunctions of boundary value problems for various equations of elliptic and mixed types in the plane, among which the works [13], [14], and others should be mentioned. Problems of this type for three-dimensional elliptic and mixed equations are also well studied, for example, in works [15], [16], [17], [18], [19], [20], [21].…”

“…Consequently, function (32) satisfies the first condition (21). Now let us show that function (32) satisfies the second condition (21). To this end, consistently using the following formulas for the hypergeometric function [5] F (a, b; c;…”

“…Assuming in (32) v = v l , l ∈ N, we obtain the eigenfunctions of the problem { (20), (21)} corresponding to eigenvalues χ l :…”