Hyers-Ulam Stability of Linear and Nonlinear Differential Equations of Second Order

Abstract

In this paper we established the Hyers-Ulam stability of a nonlinear differential equation of second order with initial condition. We also proved the Hyers -Ulam stability of a linear differential equation of second order with initial condition.

Some properties of second order differential equations

“…Proof. Suppose that z ∈ C 2 (I), such that |z (t)| ≤ |z(t)| and satisfies the inequality (14) with initial condition (4). From the Theorem 2 it follows that (20) has the Hyers-Ulam-Rassias stability with initial condition (19) and according to the substitution in Lemma 3 it follows that (5) has the Hyers-Ulam-Rassias stability with initial condition (4).…”

Hyers-Ulam-Rassias Instability for Linear and Nonlinear Systems of Differential Equations

“…In [19] Brillouët-Belluot indicated that there are only few outcomes of which we could say that they concern nonstability of functional equations. However in [20]…”

Hyers–Ulam stability of linear fractional differential equations with variable coefficients

“…Over the past decades, numerous papers on Hyers-Ulam stability have been published, especially in ordinary differential equations (ODEs) [4][5][6][7][8]. There are fruitful results in ODEs, including linear and nonlinear equations.…”