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Related papers: Hyperstability of a functional equation

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In this paper we establish the stability of the functional equation $$f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y)),\;\; x,y \in G, $$where $G$ is an abelian group.

Commutative Algebra · Mathematics 2018-10-25 Ajebbar Omar , Elqorachi Elhoucien , Themistocles M. Rassias

The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as…

Analysis of PDEs · Mathematics 2025-12-10 I. Kmit , N. Lyul'ko

We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…

Dynamical Systems · Mathematics 2026-05-22 Kai Diethelm , Safoura Hashemishahraki

We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…

Dynamical Systems · Mathematics 2008-10-14 Martin Andersson

Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…

Classical Analysis and ODEs · Mathematics 2025-09-30 Oleg Asipchuk , Laura De Carli , Weilin Li

The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust…

Systems and Control · Computer Science 2012-12-18 Zhuang Jiao , Yisheng Zhong

Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…

Statistical Finance · Quantitative Finance 2017-11-10 Petr Jizba , Jan Korbel , Hynek Lavička , Martin Prokš , Václav Svoboda , Christian Beck

A probabilistic approach to the stable matching problem has been identified as an important research area with several important open problems. When considering random matchings, ex-post stability is a fundamental stability concept. A…

Computer Science and Game Theory · Computer Science 2026-02-23 Haris Aziz , Gergely Csáji , Péter Biró

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

Dynamical Systems · Mathematics 2016-12-14 Nicholas Apostolopoulos , Fernando Ortega , Grigoris Kalogeropoulos

Let $\Omega$ be a bounded domain of $\mathbb{R}^{N}$, and $Q=\Omega \times(0,T).$ We first study the problem \[ \left\{ \begin{array} [c]{l}% {u_{t}}-{\Delta_{p}}u=\mu\qquad\text{in }Q,\\ {u}=0\qquad\text{on }\partial\Omega\times(0,T),\\…

Analysis of PDEs · Mathematics 2013-12-06 Marie-Françoise Bidaut-Véron , Hung Nguyen Quoc

Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…

Dynamical Systems · Mathematics 2018-08-24 N. D. Cong , T. S. Doan , H. T. Tuan

A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…

Mathematical Physics · Physics 2015-03-03 Oskar Sultanov

The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…

Analysis of PDEs · Mathematics 2023-12-21 Christoph Walker

We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…

Dynamical Systems · Mathematics 2017-05-16 Pawel Hitczenko , Georgi S. Medvedev

We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…

Analysis of PDEs · Mathematics 2017-09-29 Martin Gugat , Vincent Perrollaz , Lionel Rosier

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…

Mathematical Physics · Physics 2007-05-23 S. Gutman , A. G. Ramm , W. Scheid

Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…

Dynamical Systems · Mathematics 2025-06-24 Weiwei Qi , Zhongwei Shen , Yingfei Yi

This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…

Dynamical Systems · Mathematics 2011-04-08 Ivo Petras

We investigate the stability of the holographic description of the universe. By treating the perturbation globally, we discover that this description is stable, which is support for the holographic description of the universe.

High Energy Physics - Theory · Physics 2013-04-02 Peng Huang , Yong-chang Huang

We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…

Quantum Physics · Physics 2023-05-31 Xuanloc Leu , Xuan-Hoai Thi Nguyen , Jinhyoung Lee