Related papers: Stability Theory for Nullity and Deficiency of Lin…
We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays $$ \dot{x}(t)-a(t)\dot{x}(g(t))+b(t)x(h(t))=0, $$ where $$ |a(t)|<1,~ b(t)\geq 0,…
We consider perturbations of closed Friedmann universes. Perturbation modes of two lowest wavenumbers ($L=0$ and $1$) are generally known to be fictitious, but here we show that both are physical. The issue is more subtle in Einstein static…
In this paper we study the stability of two different problems. The first one is a one-dimensional degenerate wave equation with degenerate damping, incorporating a drift term and a leading operator in non-divergence form. In the second…
Facts happen at every interaction, but they are not absolute: they are relative to the systems involved in the interaction. Stable facts are those whose relativity can effectively be ignored. In this work, we describe how stable facts…
This paper introduces the concept of Hyers-Ulam stability for linear relations in normed linear spaces and presents several intriguing results that characterize the Hyers-Ulam stability of closed linear relations in Hilbert spaces.…
Bistability, or the coexistence of two stable phases, can be broken by a bias field $h$ destabilising one of the phases via the nucleation and growth of defects. Strong long-range interactions, $1/r^\alpha$ with $\alpha$ less than the…
Voltage instability is a major threat in power system operation. The growing presence of constant power loads significantly aggravates this issue, hence motivating the development of new analysis methods for both existence and stability of…
The stability of the fundamental defects of an unstretchable flat sheet is examined. This involves expanding the bending energy to second order in deformations about the defect. The modes of deformation occur as eigenstates of a…
In this chapter we consider perturbations and stability of higher dimensional black holes focusing on the static background case. We first review a gauge-invariant formalism for linear perturbations in a fairly generic class of…
The Cauchy problem for the parabolic--elliptic Keller--Segel system in the whole $n$-dimensional space is studied. For this model, every constant $A \in \mathbb{R}$ is a stationary solution. The main goal of this work is to show that $A <…
We study the positive, regular, radially symmetric solutions to the nonlinear biharmonic equation $\Delta^2 \phi = \phi^p$. First, we show that there exists a critical value $p_c$, depending on the space dimension, such that the solutions…
The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we studying in this paper is: are these singularities stable? To answer this question, we…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
We prove the nonlinear stability of the asymptotic behavior of perturbations of subfamilies of Kasner solutions in the contracting time direction within the class of polarised $T^2$-symmetric solutions of the vacuum Einstein equations with…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…
We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity and…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
In deep learning (DL) the instability phenomenon is widespread and well documented, most commonly using the classical measure of stability, the Lipschitz constant. While a small Lipchitz constant is traditionally viewed as guarantying…
We study the existence and radial stability of static, spherically symmetric thin shells separating two Schwarzschild--de Sitter spacetimes with parameters $(m_\pm,\Lambda_\pm)$. Using the Israel junction formalism and a linear barotropic…
In this expository paper, which covers material presented at the NATO Advanced Study Institute "Nonlinear Analysis, Differential Equations, and Control" (Montreal, Jul/Aug 1998), we deal with several questions related to stability and…