Periodic solutions of elasticity and electroelasticity theories for a cylinder in R3

General representations are constructed for periodic solutions of the theories of elasticity and electroelasticity for a cylinder in R³. These solutions are utilized to reduce the first boundary value problem in an unbounded isotropic medium weakened by tunnel slit cavities to a system of singular integral equations. The solvability of the characteristic part of the obtained system is proved.Sumy. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 13–20, 1990.