Boundary value problems (BVPs) of the plane elasticity posed in terms of the orientation of stresses and displacements are considered. These BVPs can be reduced to a system of homogeneous singular integral equations. Few equivalent systems are presented. They may posses a number of linearly independent solutions. The paper discusses the solvability of these equations and outlines the approach for seeking the number of solutions for the general case of 2D simple-connected domains bounded by smooth closed contours.
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