Корректность одного семейства интегральных и дифференциальных уравнений с запаздыванием, используемого в моделях живых систем

We consider a family of integral equations arising in mathematical models of some living systems. Depending on the choice of the survival of elements of living systems integral equation is reduced to the equivalent of the Cauchy problem for non-autonomous differential equations with a point or distributed delays. Problems of existence, uniqueness, nonnegativity and extendibility of solutions are investigated.