# A Neumann-type problem for the biharmonic equation

@article{Karachik2017ANP, title={A Neumann-type problem for the biharmonic equation}, author={Valery Karachik}, journal={Siberian Advances in Mathematics}, year={2017}, volume={27}, pages={103-118} }

We establish the existence and uniqueness of a solution to a Neumann-type problem in the unit ball. An illustrative example is considered.

#### 13 Citations

Riquier–Neumann Problem for the Polyharmonic Equation in a Ball

- Mathematics
- 2018

We obtain necessary and sufficient conditions for the solvability of the Riquier–Neumann problem for the inhomogeneous polyharmonic equation in the unit ball.

Neumann Type Problems for the Polyharmonic Equation in Ball

- Mathematics
- 2020

For Neumann type problems for the homogeneous polyharmonic equation in the unit ball we obtain necessary solvability conditions in the form of orthogonality of homogeneous harmonic polynomials to… Expand

On a class of Neumann type problems for polyharmonic equation

- Mathematics
- 2019

In the paper some necessary conditions for solvability of a class of Neumann type problems for polyharmonic equation in the unit ball are obtained.In the paper some necessary conditions for… Expand

On Green’s function of the Robin problem for the Poisson equation

- Mathematics
- 2018

Abstract An explicit representation of the Green function of the Robin problem for the Poisson equation in the unit ball is given.

On the Green’s Function for the Third Boundary Value Problem

- Mathematics
- 2019

We give an explicit representation of the Green’s function of the third boundary value problem for the Poisson equation in the unit ball.

On solvability of some nonlocal boundary value problems for biharmonic equation

- Mathematics
- 2020

Abstract In this paper a new class of well-posed boundary value problems for the biharmonic equation is studied. The considered problems are nonlocal boundary value problems of Bitsadze- -Samarskii… Expand

Class of Neumann-Type Problems for the Polyharmonic Equation in a Ball

- Mathematics
- 2020

Abstract A set of necessary solvability conditions for the class $${{\mathcal{N}}_{k}}$$ of Neumann-type problems for the polyharmonic equation with a polynomial right-hand side in the unit ball is… Expand

On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation

- Mathematics, Computer Science
- Symmetry
- 2019

The uniqueness and existence of a regular solution of the problem are proved and the spectral decomposition method is used to prove the main result. Expand

Green's function of Dirichlet problem for biharmonic equation in the ball

- Mathematics
- 2019

ABSTRACT An explicit representation of the Green's function of the Dirichlet problem for the biharmonic equation in the unit ball is given. Expansion of the constructed Green's function in the… Expand

The Green Function of the Dirichlet Problem for the Biharmonic Equation in a Ball

- Mathematics
- 2019

An elementary solution of the biharmonic equation is defined. By using the properties of the Gegenbauer polynomials, series expansions of this elementary solution and an associated function with… Expand

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