J4 ›› 2011, Vol. 46 ›› Issue (8): 59-62.

• Articles • Previous Articles     Next Articles

Oscillation of second order difference equations with positive and negative coefficients

YANG Jia-shan, SUN Wen-bing   

  1. Department of Science and Information, Shaoyang University, Shaoyang 422004, Hunan, China
  • Received:2010-10-05 Online:2011-08-20 Published:2011-09-08


The oscillation of a class of second order nonlinear neutral variable delay difference equation with positive and negative coefficients is discussed. Using the fixed point theorem in Banach space, a new nonoscillation criteria for the equation is obtained by introducing parameter function and the generalized Riccati transformation. Also, a sufficient condition for oscillation of the equation is proposed. These criteria can improve the restriction of the conditions for the equation, which promote some existed results.

Key words: positive and negative coefficient; neutral difference equation; variable delay; nonlinear; oscillation and nonoscillation; Riccati transformation

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