A review of the matrix Riccati equation
A sampling theorem associated with boundary-value problems with not necessarily simple eigenvalues.
A Schur method for the solution of the matrix Riccati equation.
A second order SDE for the Langevin process reflected at a completely inelastic boundary
It was shown in [2] that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog.
A second-order boundary value problem with nonlinear and mixed boundary conditions: existence, uniqueness, and approximation.
A second-order impulsive Cauchy problem.
A simple complement to Miklusiński's operational calculus
A simple method for constructing non-liouvillian first integrals of autonomous planar systems
We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.
A singular initial value problem for second and third order differential equations
A singular initial value problem for the equation
We consider the problem of the existence of positive solutions u to the problem , (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.
A smooth Lyapunov function from a class- estimate involving two positive semidefinite functions
A smooth Lyapunov function from a class- estimate involving two positive semidefinite functions
We consider differential inclusions where a positive semidefinite function of the solutions satisfies a class- estimate in terms of time and a second positive semidefinite function of the initial condition. We show that a smooth converse Lyapunov function, i.e., one whose derivative along solutions can be used to establish the class- estimate, exists if and only if the class- estimate is robust, i.e., it holds for a larger, perturbed differential inclusion. It remains an open question whether...
A software package for the numerical integration of ODEs by means of high-order Taylor methods.
A spectral regularization method for a Cauchy problem of the modified Helmholtz equation.
-stabilní metody libovolně vysokého řádu
A Stationary Schrödinger-Poisson System Arising from the Modelling of Electronic Devices.
A stochastic min-driven coalescence process and its hydrodynamical limit
A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably renormalized version of this process to a deterministic hydrodynamical limit is shown and the time evolution of the minimal size is studied for both deterministic and stochastic models.
A strong relaxation theorem for maximal monotone differential inclusions with memory
We consider maximal monotone differential inclusions with memory. We establish the existence of extremal strong and then we show that they are dense in the solution set of the original equation. As an application, we derive a “bang-bang” principle for nonlinear control systems monitored by maximal monotone differential equations.
A study of second order differential inclusions with four-point integral boundary conditions
In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of second order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
A sufficient condition for the existence of multiple periodic solutions of differential inclusions