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العنوان
On the Oscillatory Behavior of Solutions of Third-order Differential Equations /
المؤلف
Salem, Shaimaa Abd El-Badee Ahmed.
هيئة الاعداد
باحث / شيماء عبدالبديع أحمد سالم
مشرف / محمد محمود الشيخ
مناقش / حسن أحمد حسن عجوه
مناقش / عبد الكريم عبد الرحيم سليمان
الموضوع
Logic circuits. Logic design.
تاريخ النشر
2016.
عدد الصفحات
166 p. :
اللغة
الإنجليزية
الدرجة
ماجستير
التخصص
الرياضيات (المتنوعة)
تاريخ الإجازة
1/7/2016
مكان الإجازة
جامعة المنوفية - كلية العلوم - الرياضيات البحته
الفهرس
Only 14 pages are availabe for public view

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Abstract

In this thesis, we discuss the oscillatory behavior of solutions of the third order mixed neutral di erential equation a(t) 􀀀 b(t) (x(t) + p1(t)x( 1(t)) + p2(t)x( 2(t)))0 0 0 + q(t)f( x(t) + p1(t)x( 1(t)) + p2(t)x( 2(t))) = 0; t t0; where
is a non-negative constant and is the ratio of two odd positive integers. We introduce new su cient conditions for oscillation of solutions of the follow- ing forced third order di
erential equation a(t) b(t) (x(t) + p1(t)x( 1(t)) + p2(t)x( 2(t))) 0 0 0 + q(t)f( x(t) + p1(t)x( 1(t)) + p2(t)x( 2(t))) = h(t); t t0; where h(t) 2 C ([t0;1);R). Moreover, we study the oscillatory behavior of solutions of the nonlinear third order di
erential equation a(t) ” x(t) + Xn j=1 pj(t)x( j(t)) !00# !0 + Xm i=1 fi (t; x( i(t))) = 0; t t0; where 1R t0 a 􀀀1 (t)dt = 1 or 1R t0 a 􀀀1 (t)dt < 1. The obtained results improve and extend some known results in the literature. We give some examples that satisfy our results.