相关论文: On the solutions to linear systems of moment diffe…
We revisit the classical problem of construction of a fundamental system of solutions to a linear ODE whose elements remain analytic and linearly independent for all values of the roots of the characteristic polynomial.
Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expensive to compute. In this paper, we derive analytic…
The aim of this paper is to employ variational techniques and critical point theory to prove some conditions for the existence of solutions to nonlinear impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also we will…
We investigate the solution to the logistic equation involving non-local operators in time. In the linear case such operators lead to the well-known theory of time changes. We provide the probabilistic representation for the non-linear…
Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We consider the equation $$ \dot x(t)=f(t,x(t),x(\eta(t))) $$ with a variable time-shift $\eta(t)$. Both the nonlinearity $f$ and the shift function $\eta$ are given, and are assumed to be analytic (that is, holomorphic) functions of their…
The methods are proposed for evaluation of complex dynamical systems, choice of their optimal operating modes, determination of optimal operating system from given class of equivalent systems, system's timeline behaviour analysis on the…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
We survey the state of the art on the algorithmic analysis of discrete linear dynamical systems, focussing in particular on reachability, model-checking, and invariant-generation questions, both unconditionally as well as relative to…
We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows…
We use a multi-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain.
Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown that the solution map of a linear Hamiltonian system with…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
We consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms and involve abstract gradient and divergence terms. Our main interest is to provide graph and…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…