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On Some Difference Equations of First Order

Abstract One considers two boundary value problems for the Laplacian and biharmonic operator in a plane sector with boundary conditions of the Dirichlet and the Neumann type on the angle sides. The system of difference equations of first order to which this problem is reduced, is explicitly written out. Certain cases of solvability for such difference equations of first order are described; it will be useful for studying similar equations.