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    Please use this identifier to cite or link to this item: http://ir.cnu.edu.tw/handle/310902800/25267


    標題: 一些帶有停留及前進特質的常微分方程式之解的振盪定理
    Oscillatory Theorem of Some Retarded and Advanced Differential Equations
    作者: 闕文賜
    貢獻者: 藥學科
    日期: 1985
    上傳時間: 2012-05-24 11:00:37 (UTC+8)
    摘要: 擴展帶有停留( Retarded)特質的高階常微分方程式( * ) ,LnX( t ) +(-1)n+1 Σi=klPi (t)Φ(X( t-Zi)=0,此處, LkX(t)=ak(t)(Lk-1 X(t)),k=1,2………………………n,( = d/ dt ),且 a0(t) = an(t) = 1 , LoX(t) = X(t),對每一 k,k= 1,2……………………n-1,ak(t) C (〔0,∞),(0,∞)),另外對每一 i =1,2…………k,Pi(t) C (〔0,∞),(0,∞)),Zi為正常數,且Φ滿足,當y≠0,則 Φ(y)/y>0,利用積分及有界函數的極限性質,證明出下列任一條件成立①,某一 i,i = 1,2…………k,∫t-zi 1/a1(Sn-1) ∫Sn-1 1/a2(Sn-2) ∫Sn-2…………∫S Pi(S)dSdS1…………dSn-1>Φ,② ∫t-z 1/a1(Sn-1) ∫Sn-1 1/a2 (Sn-2)…………∫S Σi=1 Pi(S)dS dS1…………dSn-1 >Φ,則可推出(*)之任何有界解必振盪(Oscillatory)以上,Φ = max{lim y→∞ sup y / Φ(y),lim y→-∞ Tnfy/Φ(y)},Z = min {Z1,Z2,Z3…………Zk}進而討論高階前進(Advanced)微分方程式(* *),LnX(t) - Σj=1qj(t) A(x(t+δj)) = 0 及混合型(***)Ln X(t) + (-1)Σi=1 Pi(t)Φ(X(t-2i))+(-1) Σj=1 qj(t)A(X(k+δj)) = 0,類似的振盪定理,這裏A,qj(t),δj與Φ,Pi(t),Zi有相同的性質。
    Our goal in this paper is to discuss ; using integration and the limit property of bounded, the oscillatory behavior of retarded differential equation form ( * ), LnX( t ) +(-1)n+1 Σi=klPi (t)Φ(X( t-Zi)=0,where, LkX(t)=ak(t)(Lk-1 X(t)),for k=1,2………………………n,( = d/ dt ) and Assume a0(t) = an(t) = 1 , LoX(t) = X(t),also for k= 1,2……………………n-1,ak(t) C (〔0,∞),(0,∞)) and i =1,2…………k,Zi is opsitive constant, Pi(t) C (〔0,∞),(0,∞)) and Assume y≠0,imply Φ (y)/y>0,we prove that each of the following condition (1) for same i = 1,2…………k,∫t-zi 1/a1(Sn-1) ∫Sn-1 1/a2(Sn-2) ∫Sn-2…………∫S Pi(S)dSdS1…………dSn-1> ,2 ∫t-z 1/a1(Sn-1) ∫Sn-1 1/a2 (Sn-2)…………∫S Σi=1 Pi(S)dS dS1…………dSn-1 > ,where Z = min {Z1…………Zk}Φ = max{lim y→∞ sup y / Φ(y),lim y→-∞ Tnfy/Φ(y)}imply all bounded solution of (*) oscillatory our result also extend the oscillatory behavior of advanced differenbal equation(* *),LnX(t) - Σj=1qj(t) A(x(t+δj)) = 0 及 mix type equation (***)Ln X(t) + (-1)Σi=1 Pi(t)Φ(X(t-2i))+(-1) Σj=1 qj(t)A(X(k+δj)) = 0,where A and qj(t),δj,being the same property with Φ and Pi(t),Zi.#
    關聯: 嘉南學報 11期:p.16-24
    Appears in Collections:[嘉南學報] 11期 (1985)
    [藥學系(所)] 期刊論文

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