Volume 60, Nº 12 (2024)

The paper investigates the effect of non-stationary perturbations on the stability of nonlinear nonautonomous systems with switching and impulsive effects. Sufficient conditions have been obtained to guarantee the asymptotic stability of a given equilibrium position of the initial system, and restrictions have been established under which the asymptotic stability is preserved under perturbations acting on the system. Note that the non-stationarities present both in the system itself and in perturbations can be described by unbounded functions with respect to time, as well as functions arbitrarily close to zero. It is assumed that the basic system is homogeneous in terms of the state vector. To find the required results, the second Lyapunov method is used in combination with the theory of differential inequalities.

The two-dimensional anti-Perron effect of changing all positive characteristic exponents of the linear approximation to four different negative exponents, respectively, of four non-trivial solutions of a differential system with a perturbation of higher order of smallness, has been realized.

We study the solvability of a boundary value problem for a system of five nonlinear second-order partial differential equations under given nonlinear boundary conditions, which describes the equilibrium state of elastic non-flat inhomogeneous isotropic shells with loose edges in the framework of the Timoshenko shear model, referred to isometric coordinates.The boundary value problem is reduced to a nonlinear operator equation with respect to generalized displacements in Sobolev space, the solvability of which is established using the principle of compressed mappings.

We consider the Dirichlet problem in the hyperbolic space for a nonlinear equation of the second order with measure-valued potential. The assumptions on the structure of the equation are stated in terms of a generalized