A remark to the Floquet theorem for systems of linear differential equations
A remarkable periodic solution of the three-body problem in the case of equal masses.
A representation theorem for the linear quasi-differential equation .
A resonance problem for nonlinear Duffing equation
A Riccati technique for proving oscillation of a half-linear equation.
A Role of Abel's Equation in the Stabitity Theory of Differential Equations
A role of the coefficient of the differential term in qualitative theory of half-linear equations
The aim of this contribution is to study the role of the coefficient in the qualitative theory of the equation , where with . We discuss sign and smoothness conditions posed on , (non)availability of some transformations, and mainly we show how the behavior of , along with the behavior of the graininess of the time scale, affect some comparison results and (non)oscillation criteria. At the same time we provide a survey of recent results acquired by sophisticated modifications of the Riccati...
A second look at the first result of Landesman-Lazer type.
A second order ODE with a nonlinear final condition.
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 simple model of thermoelectric oscillations
A system of ordinary differential equations modelling an electric circuit with a thermistor is considered. Qualitative properties of solution are studied, in particular, the existence and nonexistence of time-periodic solutions (the Hopf bifurcation).
A simple proof of a semi-Fredholm principle for periodically forced systems with homogeneous nonlinearities
A singular initial value problem for second and third order differential equations
A singular ODE related to quasilinear elliptic equations.
A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations
We extend the classical Leighton comparison theorem to a class of quasilinear forced second order differential equations where the endpoints , of the interval are allowed to be singular. Some applications of this statement in the oscillation theory of (*) are suggested.
A stability criterion for periodic systems with first integrals
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 stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms. I.
A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms. II.
A Sturm separation theorem for a linear -th order self-adjoint differential equation.