一类二阶连续参数非线性差分方程的振动准则

Zhao Yu-ping
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摘要

用振动理论研究了一类二阶连续参数非线性差分方程的振动判据。然后建立了该方程所有解的振动性和解的一阶差分性的充分条件。利用Banach空间中的不动点定理,研究了该方程的非振荡解,得到了该方程在特殊条件下的正解。
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Oscillation Criteria for a Family of Second Order Nonlinear Difference Equations with Continuous Arguments
Oscillation criteria for a family of second order nonlinear difference equations with continuous arguments is studied by theory of oscillation.Then some sufficient conditions for the oscillations of all solutions and first order difference of solutions of this equation are established.Using the fixed point theorem in Banach space,the non-oscillatory solution of the equation is studied and positive solution of the equation in special conditions is obtained.
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