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This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.
We consider the problem of finding the shortest possible period for an exactly periodic solution to some given autonomous ordinary differential equation. We show that, given a pair of Lyapunov-like observable functions defined over the…
As a consequence of the main result of this paper efficient conditions guaranteeing the existence of a $T-$periodic solution to the second order differential equation \begin{equation*} u"=\frac{h(t)}{u^{\lambda}} \end{equation*} are…
In this paper we investigate existence and characterization of non-radial pseudo-radial (or separable) solutions of some semi-linear elliptic equations on symmetric 2-dimensional domains. The problem reduces to the phase plane analysis of a…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
Lam\'e's differential equation is a linear differential equation of the second order with a periodic coefficient involving the Jacobian elliptic function ${\rm sn}$ depending on the modulus $k$, and two additional parameters $h$ and $\nu$.…
Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
We introduce two ordinary second-order linear differential equations of the Laguerre- and Jacobi-type. Solutions are written as infinite series of square integrable functions in terms of the Laguerre and Jacobi polynomials, respectively.…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…
We introduce a finite difference and $q$-difference analogues of the Asymptotic Iteration Method of Ciftci, Hall, and Saad. We give necessary, and sufficient condition for the existence of a polynomial solution to a general linear…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
We prove the existence and multiplicity of periodic solutions of bouncing type for a second-order differential equation with a weak repulsive singularity. Such solutions can be catalogued according to the minimal period and the number of…
For a second-order elliptic equation in divergence form we investigate conditions on the coefficients which imply that all solutions are Lipschitz continuous or differentiable at a given point. We assume the coefficients have modulus of…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
The goal of this paper is to give a simple proof of the convergence to time-periodic states of the solutions of time-periodic Hamilton-Jacobi equations on the circle with convex Hamiltonian. Note that the period of the limiting solutions…
We study properties of basic solutions in systems with dime delays and $S^1$-symmetry. Such basic solutions are relative equilibria (CW solutions) and relative periodic solutions (MW solutions). It follows from the previous theory that the…
We investigate the scalar autonomous equation with two discrete delays $$ \dot{x}(t)=f(x(t),x(t-r),x(t-\sigma)), $$ where $f:\mathbb{R}^3\rightarrow \mathbb{R}$ is a continuously differentiable non-linear function such that $f(0,0,0)=0$. It…