TY - JOUR AU - Tang, X. H. PY - 2001/12/31 Y2 - 2024/03/29 TI - Oscillation for nonlinear delay difference equations JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 32 IS - 4 SE - Papers DO - 10.5556/j.tkjm.32.2001.342 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/342 SP - 275-280 AB - <p class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-pagination: widow-orphan;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana; mso-bidi-font-family: 新細明體; mso-font-kerning: 0pt;">The oscillatory behavior of the first order nonlinear delay difference equation of the form </span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-pagination: widow-orphan;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana; mso-bidi-font-family: 新細明體; mso-font-kerning: 0pt;">$$ x_{n+1} - x_n + p_n x_{n-k}^{\alpha} = 0, ~~~ n = 0, 1, 2, \ldots&nbsp;~~~~~~~&nbsp;\eqno{(*)} $$ </span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-pagination: widow-orphan;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana; mso-bidi-font-family: 新細明體; mso-font-kerning: 0pt;">is investigated. A necessary and sufficient condition of oscillation for sublinear equation (*) ($ 0 &lt; \alpha &lt; 1 $) and an almost sharp sufficient condition of oscillation for superlinear equation (*) ($ \alpha &gt; 1 $) are obtained.</span></p> ER -