卷 60, 编号 8 (2024)

An example of non-one-dimensional autonomous differential system is constructed, in which, on the one hand, all solutions starting in the exterior of the unit ball, tend to zero with unlimited growth of time, and on the other hand, a relative measure of the initial conditions of those solutions that begin in the ball with a center at the zero and move away from it at a sufficient distance with increasing time, approaches arbitrary close to unity as the radius of the ball tends to zero. The nonlinear system constructed in this work also has a zero linear approximation along the zero solution.

We consider a multidimensional system of ordinary differential equations with relay nonlinearity of a hysteresis type in a special form that has made it possible to analytically calculate the fixed point of the operator generated by this system. We propose procedures for selecting a vector defining the location of discontinuity surface (switch surfaces) in the phase space such that there exists a unique fixed point on one of these surfaces. Examples representing the obtained theoretical results are given.

The question of the unambiguous solvability of a non-local boundary value problem with conditions of the Bitsadze–Samarskii and Frankl type for a mixed type equation with singular coefficients is investigated.

In this paper the Fragmen-Lindelof type theorems for biharmonic functions are proved.

The parametric eigenvalue problem in infinite-dimensional Hilbert space arising in the mechanics of loaded thin-walled structures is investigated. Asymptotic properties of solutions depending on loading parameters are established. The initial infinite-dimensional problem is approximated in a finitedimensional subspace. Theoretical error estimates of approximate solutions are obtained. Effective numerical methods for calculating the main resonance frequency and the corresponding resonance form of vibrations based on asymptotic formulas are proposed.

The paper examines entire solutions of differential equations of Brio–Bouquet type. It is shown that (under some conditions that the polynomials

Ниже публикуются краткие аннотации докладов, состоявшихся в весеннем семестре 2024 г. (предыдущее сообщение о работе семинара дано в журнале “Дифференц. уравнения”. 2024. Т. 60. № 2; за дополнительной информацией обращаться по адресу: iline@cs.msu.ru)