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.
Javadian,A . (2015). Approximately $n$-order linear differential equations. International Journal of Nonlinear Analysis and Applications, 6(1), 135-139. doi: 10.22075/ijnaa.2015.224
MLA
Javadian,A . "Approximately $n$-order linear differential equations", International Journal of Nonlinear Analysis and Applications, 6, 1, 2015, 135-139. doi: 10.22075/ijnaa.2015.224
HARVARD
Javadian A. (2015). 'Approximately $n$-order linear differential equations', International Journal of Nonlinear Analysis and Applications, 6(1), pp. 135-139. doi: 10.22075/ijnaa.2015.224
CHICAGO
A Javadian, "Approximately $n$-order linear differential equations," International Journal of Nonlinear Analysis and Applications, 6 1 (2015): 135-139, doi: 10.22075/ijnaa.2015.224
VANCOUVER
Javadian A. Approximately $n$-order linear differential equations. IJNAA. 2015;6(1):135-139. doi: 10.22075/ijnaa.2015.224
International Journal of Nonlinear Analysis and Applications