Related papers: On oscillations of nonautonomous linear impulsive …
The aim of this paper is to study large deviations for the self-similar solution of a Kac-type kinetic equation. Under the assumption that the initial condition belongs to the domain of normal attraction of a stable law of index $\alpha <2$…
In this paper, ordinary and exponential dichotomies are defined in differential equations with equations with piecewise constant argument of general type. We prove the asymptotic equivalence between the bounded solutions of a linear system…
Existence and uniqueness theorems for quantum stochastic differential equations with nontrivial initial conditions are proved for coefficients with completely bounded columns. Applications are given for the case of finite-dimensional…
In this work, we present a method of generating a class of nonlinear ordinary differential equations (ODEs), representing the dynamics of appropriate nonlinear oscillators, that have the characteristics of either amplitude independent…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
In this paper are provided some sufficient conditions for a non autonomous scalar differential equation to have saddle node, transcritical and pitchfork bifurcations using higher order derivatives.
The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…
State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses…
We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a…
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides…
By folding nonautonomous differential systems in the plane to scalar differential equations, a sufficient condition for the non-occurrence of chaotic behavior is obtained.
We analyze recent results for a harmonic oscillator in an environment with a pointlike defect. We show that the allowed oscillator frequencies predicted by the authors stem from a misinterpretation of the exact solutions of a conditionally…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…
Normality arguments are applied to study the oscillation of solutions of $f''+Af=0$, where the coefficient $A$ is analytic in the unit disc $\mathbb{D}$ and $\sup_{z\in\mathbb{D}} (1-|z|^2)^2|A(z)| < \infty$. It is shown that such…
This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
In this paper we prove a variation of constants formula for a non autonomous and non homogeneous Cauchy problems whenever the linear part is not densely defined and is not a Hille-Yosida operator. By using this variation of constants…
This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation…