Fundamental Solutions of the Generalized Helmholtz Equation with Several Singular Coefficients and Confluent Hypergeometric Functions of Many Variables

Ergashev, Tuhtasin

doi:10.1134/s1995080220010047

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Existence Of a Solution Of The Neumann Problem2

−2βγ1

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2020

2022

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Cited by 13 publications

(3 citation statements)

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“…where ν k (x k ) are functions, defined in (8) and q (x, ξ) is fundamental solution of equation ( 2) [3,17]:…”

Section: Existence Of a Solution Of The Neumann Problemmentioning

confidence: 99%

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Lauricella hypergeometric function and its application to the solution of the Neumann problem for a multidimensional elliptic equation with several singular coefficients in an infinite domain

Ergashev,

Tulakova

2021

Preprint

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At present, the fundamental solutions of the multidimensional elliptic equation with the several singular coefficients are known and they are expressed in terms of the Lauricella hypergeometric function of many variables. In this paper we study the Neumann problem for a multidimensional elliptic equation with several singular coefficients in the infinite domain. Using the method of the integral energy the uniqueness of solution has been proved. In the course of proving the existence of the explicit solution of the Neumann problem, a differentiation formula, some adjacent and limiting relations for the Lauricella hypergeometric functions and the values of some multidimensional improper integrals are used.

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“…where ν k (x k ) are functions, defined in (8) and q (x, ξ) is fundamental solution of equation ( 2) [3,17]:…”

Section: Existence Of a Solution Of The Neumann Problemmentioning

confidence: 99%

“…Let us show that the function (17) satisfies the conditions (8) of the Neumann problem as for j = k and for j = k.…”

Section: Existence Of a Solution Of The Neumann Problemmentioning

confidence: 99%

See 1 more Smart Citation

Lauricella hypergeometric function and its application to the solution of the Neumann problem for a multidimensional elliptic equation with several singular coefficients in an infinite domain

Ergashev,

Tulakova

2021

Preprint

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Potentials for Three-Dimensional Singular Elliptic Equation and Their Application to the Solving a Mixed Problem

Ergashev¹

2020

Lobachevskii J Math

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Self-Similar Solutions of Some Model Degenerate Partial Differential Equations of the Second, Third, and Fourth Order

Ruzhansky

Hasanov²

2020

Lobachevskii J Math

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Fundamental Solutions of the Generalized Helmholtz Equation with Several Singular Coefficients and Confluent Hypergeometric Functions of Many Variables

Cited by 13 publications

References 14 publications

Lauricella hypergeometric function and its application to the solution of the Neumann problem for a multidimensional elliptic equation with several singular coefficients in an infinite domain

Lauricella hypergeometric function and its application to the solution of the Neumann problem for a multidimensional elliptic equation with several singular coefficients in an infinite domain

Potentials for Three-Dimensional Singular Elliptic Equation and Their Application to the Solving a Mixed Problem

Self-Similar Solutions of Some Model Degenerate Partial Differential Equations of the Second, Third, and Fourth Order

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