Generalized Hyers-Ulam stability of second-order linear differential equations using Laplace transform

A. Ponmana Selvan and M. Onitsuka

The purpose of this paper is to study the Hyers–Ulam stability and the Hyers–Ulam–Rassias stability of
homogeneous and nonhomogeneous second-order linear differential equations applying Laplace transform
method. In particular, our results can guarantee stability over unbounded intervals, and in special cases the
obtained Hyers–Ulam constants match the best Hyers–Ulam constants. In addition, the results obtained
are conditioned on the convergence of the Laplace transform of some function.

Rocky Mountain Journal of Mathematics

56

1

1

11

https://doi.org/10.1216/rmj.2026.56.1