On the n-th order iterative ordinary linear differential equations.
On the number of limit cycles in perturbations of a two dimensional nonlinear differential system.
On the number of limit cycles of a generalized Abel equation
New results are proved on the maximum number of isolated -periodic solutions (limit cycles) of a first order polynomial differential equation with periodic coefficients. The exponents of the polynomial may be negative. The results are compared with the available literature and applied to a class of polynomial systems on the cylinder.
On the number of periodic solutions of a generalized pendulum equation
For a generalized pendulum equation we estimate the number of periodic solutions from below using lower and upper solutions and from above using a complex equation and Jensen’s inequality.
On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations
We study singularly perturbed 1D nonlinear Schrödinger equations (1.1). When has multiple critical points, (1.1) has a wide variety of positive solutions for small and the number of positive solutions increases to as . We give an estimate of the number of positive solutions whose growth order depends on the number of local maxima of . Envelope functions or equivalently adiabatic profiles of high frequency solutions play an important role in the proof.
On the number of solutions of boundary value problems involving the -Laplacian.
On the Number of Solutions of the Equation ...= ...aj(t)xj, 0...t...1, for which x(0) = x(1).
On the number of zeros of bounded nonoscillatory solutions to higher-order nonlinear ordinary differential equations
The higher-order nonlinear ordinary differential equation is considered and the problem of counting the number of zeros of bounded nonoscillatory solutions satisfying is studied. The results can be applied to a singular eigenvalue problem.
On the number of zeros of Melnikov functions
We provide an effective uniform upper bound for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field. The bound depends on degrees of the field and of the perturbation, and on the order of the Melnikov function. The generic case was considered by Binyamini, Novikov and Yakovenko [BNY10]. The bound follows from an effective construction of the Gauss-Manin connection for iterated integrals.
On the numerical solution of implicit two-point boundary-value problems
On the numerical solution of nonlinear partial differential equations on divergence form
On the Numerical Treatment of a Small Divisor Problem.
On the operator equation with unbounded operators , , and .
On the opial type criterion for the well-posedness of the Cauchy problem for linear systems of generalized ordinary differential equations
The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense , with a unique solution is considered....
On the Optimal Control of a Class of Time-Delay System
In this work we study the optimal control problem for a class of nonlinear time-delay systems via paratingent equation with delayed argument. We use an equivalence theorem between solutions of differential inclusions with time-delay and solutions of paratingent equations with delayed argument. We study the problem of optimal control which minimizes a certain cost function. To show the existence of optimal control, we use the main topological properties...
On the optimality of double-bracket flows.
On the Optimum Choice of Weight Functions in a Class of Variational Calculations.
On the Order Conditions of Runge-Kutta Methods with Higher Derivatives.
On the Order of Growth of Meromorphic Solutions of First-Order Differential Equations.
On the order reduction of optimal control systems