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

Title & Authors
OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH 'SUMMATION SMALL' COEFFICIENT
KANG, GUOLIAN;

Abstract
We consider the second-order nonlinear difference equation (1) $\small{\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0}$ where $\small{{a_n},\;{p_n}}$ 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;
Language
English
Cited by
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