Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations

الملخص EN

We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form y′′+p(x)y′+q(x)y=f(x), with condition that there exists a nonzero y1:I→X in C2(I) such that y1′′+p(x)y1′+q(x)y1=0 and I is an open interval.

As a consequence of our main theorem, we prove the generalized Hyers-Ulam stability of several important well-known differential equations.