We use the second approximation of the averaging method for the investigation of stability of a system of weakly coupled oscillators with delay. A sufficient condition for the stability (instability) of a linear system of difference-differential equations is obtained.
We establish conditions for the existence of solutions of quasilinear integral equations with quasilinear constraints and substantiate the applicability of the iterative method to these equations.
For a second-order ordinary differential equation whose right-hand side contains a sum of terms with nonlinearities regularly varying with respect to the unknown function and its derivatives, we establish necessary and sufficient conditions for the existence of a broad class of monotone solutions and obtain exact asymptotic representations of solutions of this class in a neighborhood of a singular point.
We establish conditions for the existence of bounded solutions of nonlinear difference equations.
We establish necessary and sufficient conditions for the existence of solutions of a weakly nonlinear Noether boundary-value problem for a system of ordinary delay differential equations in the critical case.
We obtain conditions for the permanence and existence of a positive, asymptotically stable, piecewisecontinuous, almost periodic solution of the Mackey–Glass equation with almost periodic coefficients and pulse action.
We establish asymptotic properties of some types of solutions of one class of essentially nonlinear nonautonomous differential equations of the second order and find necessary and sufficient conditions for the existence of these solutions.
We establish conditions for the existence of continuous periodic solutions of systems of linear difference equations and develop a method for their construction.
We obtain asymptotic representations for one class of solutions of cyclic nonlinear systems of ordinary differential equations of more general type than the Emden–Fowler systems.
We obtain some results for the solutions of nonlinear boundary-value problems of a certain type with two-point nonlinear boundary conditions and reveal the efficiency of the procedure of reduction of the analyzed problem to a parametrized boundary-value problem with linear boundary conditions containing certain artificially introduced parameters. To study the transformed two-point problem, we propose a method based on the approximations of a special type constructed in the analytic form. It is shown that these approximations uniformly converge to a parametrized limit function and establish the relationship between this function and the exact solution. The proposed procedure leads to a certain system of algebraic equations whose solutions give numerical values of the parameters corresponding to the solution of the given two-point nonlinear boundary-value problem.
We substantiate the applicability of total and partial averaging schemes to the investigation of systems of fuzzy differential equations with a small parameter.
We propose a new method for the solution of linear degenerate systems of differential equations in which the zero eigenvalues of the matrix coefficient of the derivative are simple.
We give examples of abstract Cauchy problems proving that inclusions in a chain of functional classes are strict and disproving a sufficient condition for the solvability of the Cauchy problem published earlier.
We consider the Leont’ev dynamical model described by a system of delay differential equations. The stability of a program solution is studied by the method of Lyapunov functions with Razumikhin condition. We obtain an estimate for the convergence of solutions of the system to the program solution.
