Solvability and properties of critical points of linear Volterra integro-algebraic equations

Systems of Volterra linear integral equations with an identically degenerate matrix in the domain of definition with a principal term are considered. Such systems are now commonly referred to as integro-algebraic equations. The concept of a simple structure of integro-algebraic equations is introduced and the issues of solvability are investigated. In particular, systems are considered when there are critical points in the domain of definition. The article formalizes the concept of a critical point of such systems. A number of examples illustrating the theoretical results are given.