Leighton-Type Theorems for Nonlinear q-Difference Equations

• A. Zafer ^[2] ; I. Jadlovská ^[1] ; Z. N. Gurkan ^[2]
  1. [1] Slovak Academy of Sciences

     Slovak Academy of Sciences

     Eslovaquia

     
  2. [2] American University of the Middle East
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 6, 2025
• Idioma: inglés
• Enlaces
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• Resumen

  • In this work, we present a detailed study of Leighton type oscillation criteria for secondorder nonlinear q-difference equations, primarily assuming a monotonicity condition on the nonlinear function. The paper extends the classical Leighton oscillation theorem to nonlinear q-difference equations in both canonical and non-canonical cases, by employing an oscillation-preserving transformation. Furthermore, we show that the monotonicity condition may be avoided by imposing a sign condition on a coefficient and decomposing the nonlinear function into sum of two nonlinear functions.

    Examples are given to illustrate the importance and the applicability of the results.

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