Related papers: State-dependent Delay Differential Equations on $H…

The large-time behavior of solutions to the derivative nonlinear Schr\"{o}dinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our…

In this paper we study the well-known Khasminskii-Type Theorem, i.e. the existence and uniqueness of solutions of stochastic evolution delay equations, under local Lipschitz condition, but without linear growth condition. We then establish…

Parabolic integro-differential Kolmogorov equations with different space-dependent operators are considered in H\"{o}lder-type spaces defined by a scalable L\'{e}vy measure. Probabilistic representations are used to prove continuity of the…

Functional evolution equations are used in the modeling of numerous physical processes. In this work, our main tool is perturbation theory of strongly continuous semigroups. The advantage of this technique is that one can provide functional…

In a major advance and simplification of this field, we show that A Local Resolution of the Problem of Time - also viewable as A Local Theory of Background Independence - can at the classical level be described solely by of Lie's…

We prove the well-posedness of the Cauchy problem for the linear differential system of the form $x^{\prime}-A(t)x=f$, where $f$ is a distribution and $A$ possesses at most first-kind discontinuities together with all its derivatives…

The main purpose of this work is to characterize the almost sure local structure stability of solutions to a class of linear stochastic partial functional differential equations (SPFDEs) by investigating the Lyapunov exponents and invariant…

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…

In this paper we prove that periodic boundary-value problems (BVPs) for delay differential equations are locally equivalent to finite-dimensional algebraic systems of equations. We rely only on regularity assumptions that follow those of…

By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of…

This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…

We present algorithms and their implementation to compute limit cycles and their isochrons for state-dependent delay equations (SDDE's) which are perturbed from a planar differential equation with a limit cycle. Note that the space of…

The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a $\gamma$-H\"older continuous process with $\gamma>1/2$ (e.g. a fractional Brownian motion with Hurst parameter greater than…

In this paper, we are interested in path-dependent stochastic differential equations (SDEs) which are controlled by Brownian motion and its delays. Within this non-Markovian context, we give a H \"ormander-type criterion for the regularity…

It is shown that the Cauchy problem for the DNLS equation in the spatially periodic setting is locally well-posed in Sobolev spaces H^s(T) for s \geq 1/2. Moreover, global well-posedness is shown for s \geq 1 and data with small L^2 norm.

This paper proposes an unconditionally stable numerical method for solving a nonlinear Sobolev model with distributed delay. The proposed computational approach approximates the time derivative by interpolation technique whereas the spatial…

The long time behavior of solutions to the defocusing modified Korteweg-de vries (MKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method of Deift…

This document states the normal vector system for modified Hopf boundaries of delay differential systems with state and parameter dependent delays. Specifically, it states the proof for Proposition 1 in the paper entitled "Robust…

In this paper the necessary and sufficient conditions for a mapping to be the dependence of the complete solution of some differentiable first-order ordinary differential equation on the initial Cauchy condition are deduced. The result is…

We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…