Hyers–Ulam stability of linear partial differential equations of first order (original) (raw)

On the Hyers–Ulam stability of the linear differential equation

Journal of Mathematical Analysis and Applications, 2011

We obtain some results on generalized Hyers-Ulam stability of the linear differential equation in a Banach space. As a consequence we improve some known estimates of the difference between the perturbed and the exact solutions.

Hyers–Ulam stability of linear differential equations of first order, II

Applied Mathematics Letters, 2006

Let X be a complex Banach space and let I = (a, b) be an open interval. In this paper, we will prove the generalized Hyers-Ulam stability of the differential equation ty (t)+αy(t)+βt r x 0 = 0 for the class of continuously differentiable functions f : I → X, where α, β and r are complex constants and x 0 is an element of X. By applying this result, we also prove the Hyers-Ulam stability of the Euler differential equation of second order.  2005 Elsevier Inc. All rights reserved.

On Ulam–Hyers Stability for a System of Partial Differential Equations of First Order

Symmetry, 2020

The aim of this paper is to investigate generalized Ulam–Hyers stability and generalized Ulam–Hyers–Rassias stability for a system of partial differential equations of first order. More precisely, we consider a system of two nonlinear equations of first order with an unknown function of two independent variables, which satisfy the corresponding compatibility condition. The study method is that of differential inequalities of the Gronwall type.

Hyers–Ulam stability of linear differential equations of second order

Applied Mathematics Letters, 2010

We prove the Hyers-Ulam stability of linear differential equations of second order. That is, if y is an approximate solution of the differential equation y + αy + βy = 0, then there exists an exact solution of the differential equation near to y.

Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order

International Journal of Mathematics and Mathematical Sciences, 2009

The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second order y p x y q x y r x 0. That is, if f is an approximate solution of the equation y p x y q x y r x 0, then there exists an exact solution of the equation near to f.