Note on nonstability of the linear functional equation of higher order

AbstractWe provide a complete solution of the problem of Hyers–Ulam stability for a large class of higher order linear functional equations in single variable, with constant coefficients. We obtain this by showing that such an equation is nonstable in the case where at least one of the roots of the characteristic equation is of module 1. Our results are related to the notions of shadowing (in dynamical systems and computer science) and controlled chaos. They also correspond to some earlier results on approximate solutions of functional equations in single variable

A Note on Stability of an Operator Linear Equation of the Second Order

We prove some Hyers-Ulam stability results for an operator linear equation of the second order that is patterned on the difference equation, which defines the Lucas sequences (and in particular the Fibonacci numbers). In this way, we obtain several results on stability of some linear functional and differential and integral equations of the second order and some fixed point results for a particular (not necessarily linear) operator

Hyers-Ulam stability and exponential dichotomy of linear differential periodic systems are equivalent

Let $m$ be a positive integer and $q$ be a positive real number. We prove that the $m$-dimensional and $q$-periodic system \begin{equation}\tag{$\ast$} \dot x(t)=A(t)x(t),\qquad t\in\mathbb{R}_+, \qquad x(t)\in\mathbb{C}^m \end{equation} is Hyers-Ulam stable if and only if the monodromy matrix associated to the family $\{A(t)\}_{t\ge 0}$ posses a discrete dichotomy, i.e. its spectrum does not intersect the unit circle

Open-access Fishery Performance When Vessels Use Goal Achievement Behavior

While most bioeconomic models assume that vessel operators use profit maximizing behavior, it is sometimes argued that participants use other operational goals. The purpose of this paper is to compare how vessel behavior, the bioeconomic equilibrium, and the path to achieve it are changed if participants use goal achievement behavior. It is shown that, depending on the operational rule used to achieve the goal, there can be significant differences in the amount of individual vessel effort at different stock sizes, and this can affect the location and the stability of the bioeconomic equilibrium. In addition, goal achievement behavior will generally lead to a larger open-access overshoot in terms of fleet size.profit maximizing behavior, goal achievement behavior, open-access fishery behavior, Resource /Energy Economics and Policy, Q22,