Papkov S. Asymptotic evaluations of infinite systems solutions of the linear equations and their application in boundary value problems of the theory of elasticity.

The dissertation is devoted to the development of asymptotic theory of infinite systems and appli-cation of asymptotic evaluations in the problems of isotropic rods torsion (the method of stresses func-tion) and flat deformed condition of a rectangular prism (the method of superposition). The sufficient conditions of existence of a nonzero limit of the infinite system solution of the linear algebraic equations offered by B.M. Kojalovich are concerned to broader classes of infinite systems. For numerical evalua-tions of the infinite systems solutions the method of limitants was used. The problem concerning to antisymmetric prism oscillations was reduced to a quasiregular infinite system. This infinite system with the help of variables change was reduced to the set of regular infinite systems with an identical matrix which satisfy the sufficient conditions of the nonzero limit existences for their solution and to a finite system of the linear algebraic equations. The equation for defining resonance frequ encies is the finite system determination equality to zero. The stress condition of prism is analyzed as well.