On solvability of the Neumann boundary value problem for a non-homogeneous polyharmonic equation in a ball
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
Boundary Value Problems 2013, 2013:162 doi:10.1186/1687-2770-2013-162Published: 5 July 2013
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.