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Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…
We study the periodic solutions of the delay equation $\dot{x}(t)=f(x(t),x(t-1))$, where $f$ scalar is strictly monotone in the delayed component and has even-odd symmetry. We completely describe the global bifurcation structure of periodic…
We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved…
The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry…
Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show…
Time reversal symmetry is studied in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time reversal symmetry breaking in the space. On…
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mentioned, while working in the Darboux type methods, the most…
In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify these as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general…
In this paper, we establish an initial theory regarding the Second Order Asymptotical Regularization (SOAR) method for the stable approximate solution of ill-posed linear operator equations in Hilbert spaces, which are models for linear…
In this article, we build upon the work of Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190] to define a notion of a second order backward stochastic differential equation reflected on a lower c\`adl\`ag obstacle. We…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
This paper concerns a second-order differential equation with indefinite and repulsive singularities. It is the first time to study differential equation containing both indefinite and repulsive singularities simultaneously. A set of…
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest…
This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…
We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationary ergodic in time. As was proved in [24] and [12] in this case…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation…
In this paper we study the homeomorphic properties of the solutions to one dimensional backward doubly stochastic differential equations under suitable assumptions, where the terminal values depend on a real parameter. Then, we apply them…
We continue to study the 2nd-order cosmological perturbations in synchronous coordinates in the framework of the general relativity (GR) during the radiation dominated (RD) stage, and to focus on the scalar-tensor and tensor-tensor…