1 - 10 of 14 articles
We consider some classes of nonlinear mechanical systems with retarded argument. It is assumed that, in the absence of delay, the systems in question have asymptotically stable equilibria. We analyze how the delay affects the stability of these equilibria. The Lyapunov function method and...
We obtain 16 center conditions for a polynomial differential system with 27 parameters.
We consider the first main dynamic boundary value problem for a three-dimensional piecewise homogeneous hemitropic micropolar medium. By using the Fourier method under sufficiently general assumptions, we prove the solvability of the problem in the classical sense.
We obtain necessary and sufficient conditions for the representability of an evolution operator equation with the first derivative with respect to time in the form of a B
For a third-order equation of the parabolic-hyperbolic type, we suggest a method for studying a boundary value problem by solving the inverse problem for a second-order equation of the mixed parabolic-hyperbolic type with unknown right-hand side depending implicitly on time. We prove a criterion...
We construct an approximate solution of the singular integral equation with the Cauchy kernel with the use of Faber polynomials, prove its convergence to the exact solution, and indicate the order of the convergence rate.
We suggest a method for constructing asymptotic approximations to parametric families of solutions of Volterra integral equations of the first kind with piecewise smooth kernel and prove the existence of continuous solutions.
We suggest an algorithm that permits one to prove the existence of limit periodic trajectories (cycles) in two-dimensional nonautonomous dissipative systems with periodic coefficients with the use of computational methods alone. We prove a fixed point theorem for two-dimensional mappings and...
We study the solvability of a complete two-dimensional linear integral equation with a hypersingular integral understood in the sense of the Hadamard principal value. We justify the convergence of a quadrature-type numerical method for the case in which the equation in question is uniquely...
We consider two numerical methods for solving a periodic boundary value problem for a system of differential inclusions, the Galerkin method and the polygon method. To the original problem, we assign a sequence of its discretizations. Conditions under which the existence of solutions of the...
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