Ulam Stability of a Second Linear Differential Operator with Nonconstant Coefficients

Liviu Cădariu,Dorian Popa,Ioan Raşa

doi:10.3390/sym12091451

Liviu Cădariu, Dorian Popa + Show 1 more

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https://doi.org/10.3390/sym12091451

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Abstract

In this paper, we obtain a result on Ulam stability for a second order differential operator acting on a Banach space. The result is connected to the existence of a global solution for a Riccati differential equation and some appropriate conditions on the coefficients of the operator.

Highlights

Ulam stability is one of the main topics in functional equation theory
Takahasi proved that the linear differential operator of n-th order with constant coefficients is stable in Ulam sense if and only if its characteristic equation has no roots on the imaginary axis [5]
The main result on Ulam stability for the operator D defined by the relation (1) is contained in the two theorems

Summary

Introduction

Ulam stability is one of the main topics in functional equation theory. The starting point of. Takahasi proved that the linear differential operator of n-th order with constant coefficients is stable in Ulam sense if and only if its characteristic equation has no roots on the imaginary axis [5]. Popa obtained the best Ulam constant for a second order linear differential operator with constant coefficients [7]. To this moment there are few results on Ulam stability for the linear differential operator of higher order with nonconstant coefficients This is the reason for which in this paper we deal with. The number L in the relation (3) is called an Ulam constant of D

Main Result

Conclusions