具有分布时滞的偶数阶阻尼泛函微分方程的振动定理.pdfVIP

第 26卷 第2期 徐州师范大学学报(自然科学版) VoL 26，No．2 n Edition Jun．，2008 J．of Xuzhou Normal Univ．(Natura1Scie ce ) 2008年 6月 — — — — — — — — ． — — — — — ． ． ． ． ． ． ． ． ． ． ． ． ．． ． ．． ． ． ． ． ． ． ．． ． ．． ．． ．．． ．． ．．． ．． ．．． ．． ．． ．．— ． Oscillation Theorems for Differential Equations with Distributed Delay L0NG Yu—hua ，LI U Jie—chun (Department 0f Mathematics and Physics，Hu’nan Institute of Engineering，Xiangtan，Hu’nan，411104China) Abstract：In this paper，the oscillation of certain even—order damped functiona1 differentia1 equations with distributed delays is considered，and severa1 oscillation criteria are obtained for such a class of differentia1 equations using the intergra1 averaging technique and the generalized Riccati transformation．An example to illustrate our resuits is also given· Key words：even order；damped functional differential equation；distributed delay；oscillation CLC number：O175．12 Document code：A Article ID：1007—6573(2008)02—0085—05 0 Introduction Recently，there has been an increasing interest in obtaining sufficient conditions for the oscillation of solutions of second-order damped ordinary differential equations．For instance，the authors of[1—6] established oscillation theorems for the following equation： (r(t)x (￡)) +声(￡)x (t)+q(￡)f(x(￡))一0， t≥to． (1) However，very little is known for the case of higher—order damped functional differential equations with deviating arguments，especially the case with distributed deviating arguments．In this paper，we are concerned with the oscillatio