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Open Access Research

On solvability of the Neumann boundary value problem for a non-homogeneous polyharmonic equation in a ball

Batirkhan K Turmetov1* and Ravshan R Ashurov2

Author Affiliations

1 Department of Mathematics, Akhmet Yasawi International Kazakh-Turkish University, B. Sattarkhanov street, 29, Turkistan, 161200, Kazakhstan

2 Institute of Mathematics National University of Uzbekistan, Hodjaeva st., 29, Tashkent, 100125, Uzbekistan

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Boundary Value Problems 2013, 2013:162  doi:10.1186/1687-2770-2013-162

Published: 5 July 2013

Abstract

In this work the Neumann boundary value problem for a non-homogeneous polyharmonic equation is studied in a unit ball. Necessary and sufficient conditions for solvability of this problem are found. To do this we first reduce the Neumann problem to the Dirichlet problem for a different non-homogeneous polyharmonic equation and then use the Green function of the Dirichlet problem.

MSC: 35J40, 35J30, 35A01.

Keywords:
non-homogeneous polyharmonic equation; the Neumann problem; the necessary and sufficient conditions for solvability