A boundary value problem for mixed type equation with singular coefficient

В работе изучается краевая задача для уравнения смешанного типа с сингулярным коэффициентом в области, эллиптической частью которой является первая четверть плоскости, а гиперболической частью — характеристический треугольник. Методами интегральных уравнений и принципа экстремума доказывается однозначная разрешимость рассматриваемой задачи. In this paper we study a boundary value problem for a mixed type equation in a domain whose elliptic part is the first quadrant of the plane and the hyperbolic part is the characteristic triangle. With the help of the method of integral equations and the principle of extremum we prove the unique solvability of the considered problem

“Stationary” Schrödinger equation in quantum cosmology

The conditional principle of extremum in quantum cosmology is formulated for a positive functional of the energy density of space, in which gravitational constraints serve as additional conditions. The extremum conditions determine the discrete spectrum of the “stationary” state of the universe with the corresponding values of the energy density of space. A dynamic interpretation of solutions is proposed, in which the quantum number of the energy density plays the role of cosmic time. In the self-consistent harmonic approximation, the quantum dynamics of the anisotropic model of the Bianchi IX universe is considered.