Related papers: Asymptotic condition numbers for linear ordinary d…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…
The Linet-Tian metrics are solutions of the Einstein equations with a cosmological constant, $\Lambda$, that can be positive or negative. The linear instability of these metrics in the case $\Lambda <0$, has already been established. In the…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…
We investigate the large-time behavior of three types of initial-boundary value problems for Hamilton-Jacobi Equations with nonconvex Hamiltonians. We consider the Neumann or oblique boundary condition, the state constraint boundary…
This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all solutions of the pantograph equation without forcing tend to…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We analyze conditional optimization problems arising in discrete time Principal-Agent problems of delegated portfolio optimization with linear contracts. Applying tools from Conditional Analysis we show that some results known in the…
We study singularity formation in nonlinear differential equations of order $m\leqslant 2$, $y^{(m)}=A(x^{-1},y)$. We assume $A$ is analytic at $(0,0)$ and $\partial_y A(0,0)=\lambda\ne 0$ (say, $\lambda=(-1)^m$). If $m=1$ we assume…
Systems of wave equations may fail to be globally well posed, even for small initial data. Attempts to classify systems into well and ill-posed categories work by identifying structural properties of the equations that can work as…
Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general…
The aim of this work is studding the behavior of solutions of initial boundary problem for degenerated nonlinear parabolic equation of the second order, conditions of existence and non-existence in whole by time solutions, is establish.
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic…
In this paper we investigate the long time behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We consider inverse subordinators as random times and use the…
This paper studies high-order partial differential equations with random initial conditions that have both long-memory and cyclic behavior. The cases of random initial conditions with the spectral singularities, both at zero (representing…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
In this paper we investigate the long-term behaviour of solutions to the discrete Allen-Cahn equation posed on a two-dimensional lattice. We show that front-like initial conditions evolve towards a planar travelling wave modulated by a…
In this paper the asymptotic distributions are exactly solved for linearly independent solutions considering problems of the second order and for the coefficients of asymptotic destribution the recurent formulas are obtained. Further, using…