An integrating factor approach to the Hyers-Ulam stability of a class of exact differential equations of second order

Abstract

Using the integrating factor method, this paper deals with the Hyers-Ulam stability of a class of exact differential equations of second order. As a direct application of the main result, we also obtain the HyersUlam stability of a special class of Cauchy-Euler equations of second order.

The z-transform method for the Ulam stability of linear difference equations with constant coefficients

“…for each k ∈ N, where p m is defined by (22). Corollary 3.9 Let {f k } be an exponentially bounded sequence, and let p 0 , p 1 , .…”

“…As is well known, many different methods for solving differential equations have been used to study the Ulam stability of the corresponding equations, such as the integrating factor [22,25], the power series method [11], the Laplace transform [20], the method of variation of constants [23], and so on. The Laplace transform method has a significant advantage in solving linear differential equations with constant coefficients, because it can turn a differential equation into an algebraic one.…”

Fuzzy Stability of an Aqcq-Functional Equation in Matrix Fuzzy Normed Spaces

“…The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [1,3,24,31,34,35,39,42,44,50,66,57], [60]- [62]). …”

Ulam Stability for a Class of Hill’s Equations

“…For example see the works of Li and Huang [14], Li and Shen [15], and Xue [16]. On the other hand, there are many studies on the second-order linear differential equations with variable coefficients (see, [17][18][19][20][21][22][23][24]). It is well known that the most commonly encountered variable coefficient second order differential equation is Hill's equation…”