Approximately $n$-order linear differential equations

Document Type: Research Paper

Author

Semnan University, P.O. Box 35195-363, Semnan, Iran

Abstract

We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ \cdots+p_{n-1}(x)y^{\prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

Keywords