The Unique Solvability of Boundary Value Problems for a 3D Elliptic Equation With Three Singular Coefficients

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

“…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].…”

Задача Келдыша Для Трехмерного Уравнения Смешанного Типа С Тремя Сингулярными Коэффициентами

“…|y| ω nm (y)−λ nm ω nm (y) = 0, y ∈ (−a, 0)∪(0, b), т.е. уравнения (9). Следовательно ω nm (y) = Q nm (y) .…”

“…Здесь, также непосредственной проверкой можно показать, что функция P 3 nm (y) при y ∈ (−a, 0) удовлетворяет уравнению (9). Тогда, можно переписать y −2β d dy y 2β d dy P 3 nm (y) = λ nm P 3 nm (y) .…”