Hyers-Ulam stability for second-order linear differential equations with boundary conditions

Abstract

We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ eta (x) y = 0$ with $y(a) = y(b) =0$, then there exists an exact solution of the differential equation, near y.