Semi-Hyperbolicity and differential equations with infinite delay

العناوين الأخرى

شبه الزائدية و المعادلات التفاضلية ذوات التأخير اللانهائي

مقدم أطروحة جامعية

al-Maayitah, Rabia Karim

مشرف أطروحة جامعية

Badarnah, Anwar

أعضاء اللجنة

Musaidah, Basim
Rabi, Iqab Mahmud
al-Taani, Ali Ayid

الجامعة

جامعة مؤتة

الكلية

كلية العلوم

القسم الأكاديمي

قسم الرياضيات و الإحصاء

دولة الجامعة

الأردن

الدرجة العلمية

ماجستير

تاريخ الدرجة العلمية

2004

الملخص الإنجليزي

In this thesis, we review some results regarding the recently proposed, concept of Bi-shadowing in Run and in Banach spaces.

This concept is a stronger version of shadowing as it consists of direct and indirect shadowing.

It was shown in (Al-Naïf et.al., 1995) that semi-hyperbolic Lipchitz mappings in Banach space are Bi-shadowing.

In practice, this is a form of stability of solutions of certain types of differential equations, such as functional differential equations with infinite delay.

Some results, such as, a linear operator is semi-hyperbolic if and only if it is a-contracting and has no spectral values on the unit circle (theorem 2.4.4), and semi- hyperbolic mappings in Banach spaces are (a, / Bi-shadowing with respect to a-contracting comparison mappings (theorem 2.4.6), are established by Al-Naïf et.al (1996).

We apply these results to the linear differential equation with infinite delay x'(t) = Ax(i) + Bx (t-r) on the state space of initial data C° and obtain a Bi-shadowing result for this equation with respect to a non-linear perturbation of the form y'(t) = Ay (t) + By (t~r) + G {yit), yit-r y.

التخصصات الرئيسية

الرياضيات

الموضوعات

• المعادلات التفاضلية

عدد الصفحات

38

قائمة المحتويات

• APA
• MLA
• AMA

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-304448