Second method of Lyapunov and existence of periodic solutions of linear impulsive differential-difference equations.
Second order differential equations with complex-valued coefficients
Second order linear differential systems
Second Order Nonlinear Differential Equations Equivalent To Linear Differential Equations
Second order nonlinear differential equations equivalent to linear differential equations.
Second order nonlinear differential equations with linear impulse and periodic boundary conditions
In this study, we establish existence and uniqueness theorems for solutions of second order nonlinear differential equations on a finite interval subject to linear impulse conditions and periodic boundary conditions. The results obtained yield periodic solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.
Second Order Nonlinear Oscillation - Deviating Arguments.
Second phase matrix of differential systems
Self-adjoint differential equations and generalized Karamata functions
Self-equivalence 3-rd order ODEs by time-fixed transformations.
Semistability of motions and regular dependence of limit sets on points in general semi-sytems
Separation and disconjugacy.
Separatrices and singular points.
Seventy-five years of global analysis around the forced pendulum equation
Sharp estimates for the Ambrosetti-Hess problem and consequences
Motivated by [3], we define the “Ambrosetti–Hess problem” to be the problem of bifurcation from infinity and of the local behavior of continua of solutions of nonlinear elliptic eigenvalue problems. Although the works in this direction underline the asymptotic properties of the nonlinearity, here we point out that this local behavior is determined by the global shape of the nonlinearity.
Sharp inequalities for periodic functions.
Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations.
Similarity and rescaling.
Similarity solutions for high frequency excitation of liquid metal in an antisymmetric magnetic field
The aim of this paper is to investigate, as precisely as possible, a boundary value problem involving a third order ordinary differential equation. Its solutions are the similarity solutions of a problem arising in the study of the phenomenon of high frequency excitation of liquid metal systems in an antisymmetric magnetic field within the framework of boundary layer approximation.
Simple examples of one-parameter planar bifurcations.
In this paper we give simple and low degree examples of one-parameter polynomial families of planar differential equations which present generic, codimension one, isolated, compact bifurcations. In contrast with some examples which appear in the usual text books each bifurcation occurs when the bifurcation parameter is zero. We study the total number of limit cycles that the examples present and we also make their phase portraits on the Poincaré sphere.