On Hyers-Ulam-Rassias Stability for Bernoulli's and First Order Linear and Nonlinear Differential Equations

Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations

“…But in fact, in [25] ( , 0) = 0. However in our case, if the function 0 has the property 0 ( ) ≠ 0 for some point ∈ [ 0 , 1 ], then it requires that ( , 0) ≠ 0.…”

“…In the same year, Qarawani [25] established the stability of first-order linear and nonlinear differential equations in the sense of HUR. Also, he investigated stability and asymptotic stability in the sense of HUR for a differential equation of the form…”

“…Our research is inspired by the paper of Qarawani [25]. In this studied, we establish the stability in the sense of HU, HUR and HURG for the following differential equation of the form:…”

“…However in our case, if the function 0 has the property 0 ( ) ≠ 0 for some point ∈ [ 0 , 1 ], then it requires that ( , 0) ≠ 0. For example, if the function ( , ) is taken as ( , ) = 1 + 2 , then it becomes ( , 0) = 1 ≠ 0 and the condition of Qarawani's [25] becomes invalid.…”

Stability of delay differential equations in the sense of Ulam on unbounded intervals

“…In 2014, Qarawani [30] established the stability of linear and nonlinear differential equations of firstorder in the sense of Hyers-Ulam-Rassia. Also, he investigated stability and asymptotic stability in the sense of Hyers-Ulam-Rassias for a Bernoulli's differential equation.…”