Oscillation in Neutral Equations with Integrable Coefficients

• Main Authors: Yang, Chung-Ming, 楊聰敏
• Other Authors: MING-PO CHEN
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/57639612354535389593

碩士 === 輔仁大學 === 數學系研究所 === 84 === The author obtains some new sufficient conditions for the oscillation of all solutions of the next two neutral differential equations : $$(1) \qquad \frac{d}{dt}[X(t)-R(t)X(t-r)]+P(t)X(t-\tau)-Q(t)X(t-\delta)=0$$ where $P,Q,R \in C([t_0,\infty ),R^+),r\in (0,\infty ),\tau ,\delta \in R^+.$\ $$(2) \qquad \frac{d^n}{dt^n}[X(t)-R(t)X(t-r)]+P(t)X(t-\tau)-Q( t)X(t-\delta)=0$$ where $n\ge 3,n ~~\mbox{is odd} , P,Q,R \in C([t_0,\infty ),R^+),r\in (0,\infty ),\tau ,\delta \in R^+.$\ without the usual hypothesis $$\int _{t_0}^{\infty}[p(s)-Q(s-\tau+\delta)]ds=\infty$$