Решение сингулярно возмущенной задачи Коши при наличии «слабой» точки поворота у предельного оператора

The paper proposes a method for constructing an asymptotic solution of the singularly perturbed Cauchy problem in the case of violation of the stability conditions of the spectrum of the limit operator. In particular, we consider the problem with a turning point where eigenvalues "stick together" at $t=0$.