June 30 Vera V. Malygina read a course of lectures "On the stability of solutions of differential equations"

On June 30, a researcher of the Perm National Research Polytechnic University, candidate of physics and mathematics, associate professor Vera V. Malygina gave a course of lectures “On the stability of solutions of differential equations”.

In the lectures she told about the integral representation of solutions to linear systems of ordinary differential equations, about the fundamental matrix, the Cauchy matrix and their properties. Relationships were established between different types of stability of solutions with respect to initial data: Lyapunov stability, asymptotic stability, exponential stability, uniform stability, uniform asymptotic stability, uniform exponential stability. Equivalence of uniform asymptotic and uniform exponential stability was shown. Systems of ordinary differential equations with summable coefficients were considered. The equivalence of stability along the right-hand side of Lebesgue spaces and uniform exponential stability (the Bohl–Perron theorem) was proven.

The lectures were held in a mixed format: face-to-face at the Sobolev Institute of Mathematics and remotely in Google Meet. The lectures were attended by students and graduate students of Novosibirsk State University, employees of the Sobolev Institute of Mathematics and the Lavrentev Institute of Hydrodynamics.

V. V. Malygina's lectures were organized by the participants of the research project "Differential Equations and Dynamical Systems" of the Mathematical Center in Akademgorodok.