Hyers-Ulam stability of n ͭ ͪ order linear differential equation (original) (raw)
Related papers
On the Stability Problem of Differential Equations in the Sense of Ulam
Results in Mathematics, 2019
In this paper we consider the stability problem of a general class of differential equations in the sense of Hyers-Ulam and Hyers-Ulam-Rassias with the aid of a fixed point technique. We extend and improve the literature by dropping some assumptions of some well known and commonly cited results in this topic. Some illustrative examples are also given to visualize the improvement.
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 functional differential equations
Journal of Mathematical Analysis and Applications, 2015
In this paper, the stability of some classes of linear functional differential equations was discussed by direct method, iteration method, fixed point method and open mapping theorem. It is shown that the Hyers-Ulam stability holds true for y (n) = g(t)y(t − τ ) + h(t). The stability of functional differential equations with multiple delays of first order and general delay differential equations also have been discussed.
On Hyers-Ulam Stability of Nonlinear Differential Equations
Bulletin of the Korean Mathematical Society, 2015
We investigate the stability of nonlinear differential equations of the form y (n) (x) = F (x, y(x), y ′ (x),. .. , y (n−1) (x)) with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is obtained.
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.
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.
In 1940 (and 1968) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1951 D. G. Bourgin has been the second author treating the Ulam problem for additive mappings. In 1978 according to P. M. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982-2004 we established the Hyers-Ulam stability for the Ulam problem for different mappings. In this article we solve the Hyers-Ulam problem for quadratic type functional equations in several variables. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology.
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.