Non-Archimedean Stability of Nonhomogeneous Second-Order Linear Differential Equation - Stori, Mohammad Khalid (Journal of Natural Sciences – Kabul University, 2025)
For the first time in 1933, Abloza studied the stability of Hyers-Ulam linear differential equations. Since then, many articles have been published in this field, some of which can be found in references (6-19). In this paper, we investigate the stability of linear differential equations in a non-Archimedean normed space. Let (R,∥⋅∥)(R, \|·\|)(R,∥⋅∥) be a non-Archimedean normed space of real numbers. In this paper, we prove the Hyers-Ulam stability of nonhomogeneous second-order linear differential equations with non-constant coefficients, y′′+f(x)y′+g(x)y=h(x)y'' + f(x)y' + g(x)y = h(x)y′′+f(x)y′+g(x)y=h(x), in the non-Archimedean normed space (R,∥⋅∥)(R, \|·\|)(R,∥⋅∥), where f,g,h:(a,b)⊆R→Rf, g, h : (a, b) R → Rf,g,h:(a,b)⊆R→R are given continuous functions.