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OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH 'SUMMATION SMALL' COEFFICIENT

  • KANG, GUOLIAN
  • Published : 2005.05.01

Abstract

We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.

Keywords

summation small coefficient;oscillation;nonlinear difference equation

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