The initial boundary value problem of a mixed-typed hemivariational inequality.
The invariant cone of slowly oscillating solutions to two delay differential equations.
The inverse carrier problem
The problem was motivated by Borůvka’s definitions of the carrier and the associated carrier. The inverse carrier problem is precisely defined and partially solved. Examples are given.
The Kurzweil integral in financial market modeling
Certain financial market strategies are known to exhibit a hysteretic structure similar to the memory observed in plasticity, ferromagnetism, or magnetostriction. The main difference is that in financial markets, the spontaneous occurrence of discontinuities in the time evolution has to be taken into account. We show that one particular market model considered here admits a representation in terms of Prandtl-Ishlinskii hysteresis operators, which are extended in order to include possible discontinuities...
The Lie group in infinite dimension.
The Lyapunov stability for the linear and nonlinear damped oscillator with time-periodic parameters.
The magnetic geodesic flow on a homogeneous symplectic manifold.
The method of averaging and functional differential equations with delay.
The method of lower and upper solutions for th-order periodic boundary value problems.
The method of lower and upper solutions for some fourth-order equations.
The method of solution of the boundary value problem applied to a certain fourth order differential equation
The microlocal Landau-Zener formula
The minimal period problem of classical hamiltonian systems with even potentials
The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations
In this paper, we develop monotone iterative technique to obtain the extremal solutions of a second order periodic boundary value problem (PBVP) with impulsive effects. We present a maximum principle for ``impulsive functions'' and then we use it to develop the monotone iterative method. Finally, we consider the monotone iterates as orbits of a (discrete) dynamical system.
The monotonicity of extremants of integrals of the differential equation
The most general transformation of homogeneous linear differential retarded equations of the first order
The moving frames for differential equations. I. The change of independent variable
The article concerns the symmetries of differential equations with short digressions to the underdetermined case and the relevant differential equations with delay. It may be regarded as an introduction into the method of moving frames relieved of the geometrical aspects: the stress is made on the technique of calculations employing only the most fundamental properties of differential forms. The present Part I is devoted to a single ordinary differential equation subjected to the change of the independent...
The moving frames for differential equations. II. Underdetermined and functional equations
Continuing the idea of Part I, we deal with more involved pseudogroup of transformations , , applied to the first order differential equations including the underdetermined case (i.e. the Monge equation ) and certain differential equations with deviation (if is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction into the...
The multiplicity criteria for zero points of second order differential equations
The nonlinear limit-point/limit-circle problem for higher order equations
We describe the nonlinear limit-point/limit-circle problem for the -th order differential equation The results are then applied to higher order linear and nonlinear equations. A discussion of fourth order equations is included, and some directions for further research are indicated.