A comparison of four- and five-point difference approximations for stabilizing the one-dimensional stationary convection-diffusion equation.
A comparison theorem for linear delay differential equations
In this paper property (A) of the linear delay differential equation is to deduce from the oscillation of a set of the first order delay differential equations.
A comparison theorem in the theory of the second-order linear differential transformations
A completeness theorem relative to one-dimensional Schrödinger equations with energy-dependent potentials
A computational investigation of an integro-differential inequality with periodic potential.
A Computational Solution for a Matrix Riccati Differential Equation.
A constructive method for solving stabilization problems
The problem of asymptotic stabilization for a class of differential inclusions is considered. The problem of choosing the Lyapunov functions from the parametric class of polynomials for differential inclusions is reduced to that of searching saddle points of a suitable function. A numerical algorithm is used for this purpose. All the results thus obtained can be extended to cover the discrete systems described by difference inclusions.
A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions
We present a constructive proof of the fact that the set of algebraic Pfaff equations without algebraic solutions over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree.
A conterexample in the theory of linear singularly perturbed systems
A continuation method for motion-planning problems
We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...
A continuation method for motion-planning problems
We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...
A continuous version of the Filippov-Gronwall inequality for differential inclusions
We give an estimate for the distance between a given approximate solution for a Lipschitz differential inclusion and a true solution, both depending continuously on initial data.
A contribution to Runge-Kutta formulas of the 7th order with rational coefficients for systems of differential equations of the first order
The purpose of this article is to find the 7th order formulas with rational parameters. The formulas are of the 11th stage. If we compare the coefficients of the development up to with the development given by successive insertion into the formula for and we obtain a system of 59 condition equations with 65 unknowns (except, the 1st one, all equations are nonlinear). As the solution of this system we get the parameters of the 7th order Runge-Kutta formulas as rational numbers.
A contribution to the phase theory of a linear second-order differential equation in the Jacobian form
A contribution to the problem of coexistence of two periodical solutions of the Hill's equation
A contribution to the theory of stability of differential equations in Banach space
A convergence result for discrete steepest descent in weighted Sobolev spaces.
A convergence theorem on the iterative solution of nonlinear two-point boundary-value systems
A converse Lyapunov theorem and robustness with respect to unbounded perturbations for exponential dissipativity.
A counterexample to the periodic orbit conjecture