Existence, uniqueness and Ulam stability of the first-order (p, q)-difference equations

• Jietian Dong ^[1] ; JinRong Wang ^[1]
  1. [1] Guizhou University

     Guizhou University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
• Idioma: inglés
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• Resumen

  • In this paper, within the framework of (p, q)-integrals, we first obtain an estimate for increasing functions different from that in classical integrals and establish a new Gronwall inequality. Subsequently, we present the expression for the solution to the first-order linear (p, q)-difference equation and prove the existence and uniqueness of the solution to the first-order nonlinear (p, q)-difference equation. Furthermore, by employing the newly established Gronwall inequality, we study the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of the first-order (p, q)-difference equations. Finally, several illustrative examples are provided to verify the validity of the theoretical results.