Document Type : Research Paper

Author

• Abbas Javadian

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

• Hyers-Ulam stability
• Linear differential equation
• homogeneous equation