相关论文: On the solution of a second order functional diffe…

We establish a new type of local asymptotic formula for the Green's function ${\mathcal G}_t(x,y)$ of a uniformly parabolic linear operator $\partial_t - L$ with non-constant coefficients using dilations and Taylor expansions at a point…

In this paper, we analyze the solutions of the following non-linear differential-difference equations f^n(z) +\omega f^(n-1)f'(z) +p(z)f(z+c) = p_1e^{\alpha}_1z +p_2e^{\alpha}_2z and f^n(z)f'(z) +q(z)e^Q(z)f(z+c) = p_1e^{\alpha}_1z…

The dynamics of the second order rational difference equation in the title with complex parameters and arbitrary complex initial conditions is investigated. Two associated difference equations are also studied. The solutions in the complex…

Explicit numerical methods based on Lax-Friedrichs and Leap-Frog finite difference approximations are constructed to find the numerical solution of the first-order hyperbolic partial differential equation with point-wise delay or advance,…

We propose a differential difference equation in ${\mathcal R}^1\times {\mathcal Z}^2$ and study it by Hirota's bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson…

We consider linear delay differential equations at the verge of Hopf instability, i.e. a pair of roots of the characteristic equation are on the imaginary axis of the complex plane and all other roots have negative real parts. When…

In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…

We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend…

In this paper, we focus on the solvability of a class of fractional backward stochastic differential equations (BSDEs, for short) with delayed generator. In this class of equations, the generator includes not only the values of the…

This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for…

In this paper, we will develop a definition of mild solution for impulsive fractional differential equation of order $\alpha\in (1,2)$ with the help of solution operator and study the existence results of mild solution for impulsive…

In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability…

We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…

We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having indefinite integral representation. The…

Second order equations of the form $z'' + A_0 z + D z'=0$ in an abstract Hilbert space are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of…

In this paper, we analyze a second-order differential equation with a piecewise constant argument and reflection coupled to periodic boundary conditions. Our main contribution is the construction of the related Green's function and a…

We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity…

We present a condition for a stochastic differential equation dX_{t}={\mu}(t,X_{t})dt+{\sigma}(t,X_{t})dB_{t} to have a unique functional solution of the form Z(t,B_{t}). The condition expresses a relation between {\mu} and {\sigma}. A…

In this paper, we present and analyze a linear fully discrete second order scheme with variable time steps for the phase field crystal equation. More precisely, we construct a linear adaptive time stepping scheme based on the second order…

In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not…