<p>In this work, we present a detailed study of Leighton type oscillation criteria for second-order nonlinear <i>q</i>-difference equations, primarily assuming a monotonicity condition on the nonlinear function. The paper extends the classical Leighton oscillation theorem to nonlinear <i>q</i>-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.</p>

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Leighton-Type Theorems for Nonlinear q-Difference Equations

  • A. Zafer,
  • I. Jadlovská,
  • Z. N. Gurkan

摘要

In this work, we present a detailed study of Leighton type oscillation criteria for second-order 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.