Journal of Applied Mathematics (Jan 2011)
Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations
Abstract
We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form π¦ξ ξ +π(π₯)π¦ξ +π(π₯)π¦=π(π₯), with condition that there exists a nonzero π¦1βΆπΌβπ in πΆ2(πΌ) such that π¦1ξ ξ +π(π₯)π¦ξ 1+π(π₯)π¦1=0 and πΌ 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.