Abstract
By means of Riccati transformation technique, we establish some new oscillation criteria for second-order nonlinear delay difference equation
when \(\sum\limits_{n = 0}^\infty {\left( {\frac{1}{{Pn}}} \right)^{\frac{1}{\gamma }} = \infty }\). When \(\sum\limits_{n = 0}^\infty {\left( {\frac{1}{{Pn}}} \right)^{\frac{1}{\gamma }} < \infty }\) we present some sufficient conditions which guarantee that, every solution oscillates or converges to zero. When \(\sum\limits_{n = 0}^\infty {\left( {\frac{1}{{Pn}}} \right)^{\frac{1}{\gamma }} = \infty }\) holds, our results do not require the nonlinearity to be nondecreasing and are thus applicable to new classes of equations to which most previously known results are not.
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Saker, S.H. Oscillation theorems for second-order nonlinear delay difference equations. Periodica Mathematica Hungarica 47, 201–213 (2003). https://doi.org/10.1023/B:MAHU.0000010821.30713.be
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DOI: https://doi.org/10.1023/B:MAHU.0000010821.30713.be