时标上具有正负项的非线性中立型动力方程非振动解的存在性

Existence of Non-oscillatory Solutions for the Second Order Nonlinear Neutral Dynamic Equations with Positive and Negative Terms on Time Scales

基于对微分方程非振动解的存在性的研究,考虑了时标Τ上的具有正负项的二阶非线性动力方程及其对应的扰动方程非振动解的存在性,通过构造适当的映射,用Banach压缩映射原理得到它们非振动解存在的充分条件,进一步完善动力方程的振动性理论.

Based on an understanding of the existence of non - oscillation solutions of differential equations, this paper studies the existence of non - oscillatory solutions for the second order nonlinear dynamic equation with posi- tive and negative terms and its corresponding non - oscillatory solution for the perturbation equation. By defining mappings and using Banaeh＇s fixed theorem, it has obtained the existence of non - oscillatory solutions for the above equations. It has further improved the dynamic equation of the vibration theory.