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 of Nonlinear Neutral Dynamic Equations with Positive and Negative Terms on Times Scales

基于对微分方程非振动解的存在性的研究,考虑时标上的具有正负项的二阶非线性动力方程非振动解的存在性,主要通过时标上的导数积分运算,链式法则,含参量积分求导及中值定理,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 the existence of non-oscillation solutions of differential equations, the existence of non-oscillatory solutions of the second order nonlinear dynamic equation with positive and negative terms is considered. By derivative and integral operation, Chain Rule, Intermediate Value Theorem on time scales, defining mappings and Banach＇s fixed theorem, the sufficient condition of the existence of non-oscillatory solutions of the above equations is obtained. The vibration theory of the dynamic equation is further improved.