Construction of regularized asymptotics for the solution of a singularly perturbed mixed problem on the half-axis for the inhomogeneous Schrödinger-type equation with the potential $V(x)=x$

In this paper, we propose a method for constructing an asymptotic solution to a singularly perturbed mixed problem on the half-axis for a nonstationary inhomogeneous Schrödinger-type equation in the coordinate representation in the case of violation of the stability conditions for the spectrum of the limit operator. The chosen profile of the potential energy leads to a spectral singularity of the limit operator, which, within the framework of S. A. Lomov's regularization method, is usually called a strong turning point.