Hyers-Ulam Stability of a Generalized Second-Order Nonlinear Differential Equation

Abstract

In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.

Hyers-Ulam stability of abstract second order linear dynamic equations on time scales

“…In [13] Maher established the Hyers-Ulam stability of generalized nonlinear second-order differential equations and he proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.…”

Ulam–Hyers Stability of Linear Differential Equation with General Transform

“…through the Laplace transform technique. The results of the Ulam-Hyers stability for various earlier outcomes have been proved or discussed in the recent monograph [26,27] and in the papers [28][29][30]. The results obtained through general integral transform are very close to those obtained by Laplace transform [31].…”

Hyers-Ulam-Rassias stability of some perturbed nonlinear second order ordinary differential equations

“…Hyers continued where Ulam stopped and extended his result to investigate Hyers-Ulam stability [8], which was later extended again to Hyers-Ulam-Rassias stability by Rassias [21] in 1978. In these articles [1,7,10,11,12,13,14,15,16,25,27] researchers investigated the Hyers-Ulam stability of linear differential equations, while in [2,4,5,6,17,18,19,20,23,24,22] others considered Hyers-Ulam stability of nonlinear differential equations. In this paper we investigate the Hyers-Ulam-Rassias stability of the following nonlinear second order ordinary differential equation which are perturbed and of the form: £ r(t)φ(u(t))u 0 (t) ¤ 0 +g(t, u(t), u 0 (t))u 0 (t)+α(t)h(u(t)) = p(t, u(t), u 0 (t)), ∀t > 0…”