2012

İkinci Mertebeden Gecikmeli Bir Diferansiyel Denklemin Hyers-Ulam Rassias Kararlılığı

Bu çalışmada, ilk olarak bir sürekli fonksiyon ve negatif olmayan reel bir sabit olmak üzere , şeklindeki birinci mertebeden sabit gecikmeli bir diferansiyel denklemin Banach sabit nokta teoremi kullanılarak Hyers-Ulam Rassias kararlılığı gösterildi. Buradan elde edilen sonuçtan faydalanılarak sürekli fonksiyonlar olmak üzere biçimindeki ikinci mertebeden sabit gecikmeli bir diferansiyel denklemin Hyers-Ulam Rassias kararlılığı araştırıldı. Ayrıca çalışmadaki teorik analizleri açıklamak için bir örnek verildi.

Anahtar Kelimeler:

Banach Sabit Nokta Teoremi, Gecikmeli Diferansiyel Denklem, Hyers-Ulam Rassias Kararlılık

Hyers-Ulam Rassias Stability of a Second Order Delay Differential Equation

In this study, firstly, we use Banach fixed point theorem to show that the Hyers-Ulam Rassias stability of a first order delay differential equation with constant delay of the formwhere is continuous function and is a nonnegative real constant. By taking advantage of this result, we investigate Hyers-Ulam Rassias stability of a second order delay differential equation with constant delay of the form where are continuous functions and is a nonnegative real constant. Also we present an example to illustrate the theoretical analysis.

Keywords:

Banach Fixed Point Theorem, Delay Differential Equation, Hyers-Ulam Rassias Stability,

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