Approximately $n$-order linear differential equations

Document Type : Research Paper


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


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.


Volume 6, Issue 1 - Serial Number 1
March 2015
Pages 135-139
  • Receive Date: 18 January 2014
  • Revise Date: 12 November 2014
  • Accept Date: 29 December 2014