Abstract
We establish the Ulam stability of a first-order linear nonautonomous quantum equation with Cayley parameter in terms of the behavior of the nonautonomous coefficient function. We also provide details for some cases of Ulam instability.
Highlights
1 Introduction In a series of recent papers [7–9] the authors introduced the study of Ulam stability for linear quantum (q-difference) equations of first order with a complex constant coefficient
There are no works in the literature dealing with first-order linear quantum equations with nonautonomous coefficient functions, which we initiate below
The situation is clarified by presenting an example where Ulam stability breaks down if the absolute value of the variable coefficient approaches zero
Summary
1 Introduction In a series of recent papers [7–9] the authors introduced the study of Ulam stability for linear quantum (q-difference) equations of first order with a complex constant coefficient. Definition 1.1 Equation (1.1) is Ulam stable on qN0 if there is a constant C > 0 with the following property: For any ε > 0 and for any function ζ satisfying We highlight the q-difference (quantum) exponential function and its properties and provide details on the solution to the related nonhomogeneous equation.
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