Integro-differential equations with degeneration in Banach spaces and it's applications in mathematical theory of elasticity

Cauchy problem for linear integro-differential operator equation with degenerated differential part of high order and convolutional type Volterra integral term is considered in article. Fundamental operator-function of integro-differential operator, appropriated of examining equation, is constructed, Cauchy problem generalized (in class of distributios with left-bounded support) and classical ($N$ times strongly continuously differentiable) solutions existence and uniqueness theorems are proved. Obtaining results are applied to the investigation of initial boundary value problems, arised in mathematical theory of elasticity.