相关论文: Extending a theorem of Datko for evolutionary fami…

In the context of holomorphic families of ${\mathbb P}^k$ endomorphisms, we show that various notions of stability are equivalent. This allows us to both extend and simplify the architecture of the proof of certain results of [BBD]

We introduce an (evolution) algebra identifying the coefficients of inheritance of a bisexual population as the structure constants of the algebra. The basic properties of the algebra are studied. We prove that this algebra is commutative…

We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive…

In this paper, we introduce generalized dichotomies for nonautonomous random linear dynamical systems acting on arbitrary Banach spaces, and obtain their complete characterization in terms of an appropriate admissibility property. These…

Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…

Using the fixed point method of the stability of the Jensen's functional equation, we proved the Hyers-Ulam-Rassias stability and super stability of involution on Banach algebra and find some conditions that with them a Banach algebra with…

We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…

For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…

In a recent paper (Math. Ann. 393 (2025), 1769--1795), Elorreaga et al. have obtained a complete characterization of the notion of a $h$-dichotomy for ordinary differential equations on a finite-dimensional space in terms of the notions of…

This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…

We explore the numerical stability properties of an evolution system suggested by Alekseenko and Arnold. We examine its behavior on a set of standardized testbeds, and we evolve a single black hole with different gauges. Based on a…

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…

We study monotone skew-product semiflows generated by families of nonautonomous neutral functional differential equations with infinite delay and stable D-operator, when the exponential ordering is considered. Under adequate hypotheses of…

In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a…

In this note a far extension of the Banach fixed point theorem is proved.

The initial-value problem associated with multi-valued operators in Banach spaces is here reformulated as a minimization principle, extending results of Brezis-Ekeland, Nayroles and Fitzpatrick. At the focus there is the stability of these…

Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.

We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…

In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of a Cauchy-Jensen additive functional equation in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated…