The existence of periodic solutions of an autonomous second order non-linear differential equation
The first conjugate point of solution of the -th order iterated differential equation
The first derivative of period function of a plane vector field.
The algorithm of the successive derivatives introduced in [5] was implemented in [7], [8]. This algorithm is based on the existence of a decomposition of 1-forms associated to the relative cohomology of the Hamiltonian function which is perturbed. We explain here how the first step of this algorithm gives also the first derivative of the period function. This includes, for instance, new presentations of formulas obtained by Carmen Chicone and Marc Jacobs in [3].
The first kind periodic solutions of differential equations of the second order
The first, the second, and the third Liouville formula and periodical solutions of linear differential equation of the second order
The fixed point theorem and the boundedness of solutions of differential equations in the Banach space
The properties of solutions of the nonlinear differential equation in a Banach space and of the special case of the homogeneous linear differential equation are studied. Theorems and conditions guaranteeing boundedness of the solution of the nonlinear equation are given on the assumption that the solutions of the linear homogeneous equation have certain properties.
The full periodicity kernel for a class of graph maps.
The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points
The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0...
The influence of argument delay on oscillatory properties of a second-order differential equation
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