On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator.
On the existence of periodic boundary conditions for nonlinear second order differential equations
On the exponential stability of a certain Lurie system
On the Floquet theory of differential equations with a complex coefficient of the real variable
On the generalized Floquet theory of disconjugate differential equations
On the monotonicity of the period function of some second order 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 periodic boundary-value problem for systems of second-order nonlinear ordinary differential equations.
On the periodic solutions of linear homogeneous systems of differential equations.
On the Poincaré-Lyapunov constants and the Poincare series
For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial...
On the ``Poincaré-Lyapunov”-like systems of three differential equations
On the semilinear multi-valued flow under constraints and the periodic problem
In the paper we will be concerned with the topological structure of the set of solutions of the initial value problem of a semilinear multi-valued system on a closed and convex set. Assuming that the linear part of the system generates a -semigroup we show the -structure of this set under certain natural boundary conditions. Using this result we obtain several criteria for the existence of periodic solutions for the semilinear system. As an application the problem of controlled heat transfer...
On the solution set of the nonconvex sweeping process
We prove that the solutions of a sweeping process make up an -set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.
On the spectrum of weakly almost periodic solutions of certain abstract differential equations.
On the structure of second-order periodic differential equations with given characteristic multipliers
On the weakly almost periodic solutions of certain abstract differential equations
On using curvature to demonstrate stability.
One-parameter families of brake orbits in dynamical systems
We give a clear and systematic exposition of one-parameter families of brake orbits in dynamical systems on product vector bundles (where the fiber has the same dimension as the base manifold). A generalized definition of a brake orbit is given, and the relationship between brake orbits and periodic orbits is discussed. The brake equation, which implicitly encodes information about the brake orbits of a dynamical system, is defined. Using the brake equation, a one-parameter family of brake orbits...