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http://dx.doi.org/10.4134/BKMS.2005.42.2.245

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

KANG, GUOLIAN (INSTITUTE OF SYSTEM SCIENCE, ACADEMY OF MATHEMATICS AND SYSTEM SCIENCES, CHINESE ACADEMY OF SCIENCES)

Publication Information

Bulletin of the Korean Mathematical Society / v.42, no.2, 2005 , pp. 245-256 More about this Journal

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;

Citations & Related Records

Reference

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