Zaman Skalasında Fonksiyonel Dinamik Denklemlerin Alternatif Parametreler Değişimi ile h-Kararlılığı

Yıl 2022, Cilt: 11 Sayı: 2, 459 - 468, 30.06.2022

Halis Can Koyuncuoğlu Nezihe Turhan Turan

https://doi.org/10.17798/bitlisfen.1025334

Öz

Bu çalışmada, zaman skalalarında kurulmuş

x^∆ (t)=a(t)x(t)+f(t,x(t)), t∈T,

formundaki doğrusal olmayan fonksiyonel dinamik denklemlerin üzerinde durulmuş olup, bu tip denklemlerin h-kararlılığı çalışılmıştır. h-Kararlılık kavramı özel şartlar altında üstel kararlılığı, üniform kararlılığı ve Lipschitz kararlılığını kapsamaktadır. Makalenin analiz kısmında alternatif bir parametrelerin değişimi formülünün kullanılması ile odaklanılan denklemlerdeki regresiflik koşulu aranmamıştır, ve bu da daha geniş bir denklem sınıfının çalışılmasına imkan sağlamıştır. Elde edilen kararlılık sonuçlarına ek olarak, dinamik sistemlerin çözümlerinin üniform sınırlılığı ve h-kararlılığı arasındaki ilişki belirli şartlar altında elde edilmiştir.

Anahtar Kelimeler

h-Kararlılık, Zaman Skalası, Alternatif Parametrelerin Değişimi, Üniform Sınırlılık

h- Stability of Functional Dynamic Equations on Time Scales by Alternative Variation of Parameters

Öz

In this paper, we concentrate on nonlinear functional dynamic equations of the form

x^∆ (t)=a(t)x(t)+f(t,x(t)), t∈T,

on time scales and study h-stability, which implies uniform exponential stability, uniform Lipschitz stability, or uniform stability in particular cases. In our analysis, we use an alternative variation of parameters, which enables us to focus on a larger class of equations since the dynamic equations under the spotlight are not necessarily regressive. Also, we establish a linkage between uniform boundedness and h-stability notions for solutions of dynamic equations under sufficient conditions in addition to our stability results.

Anahtar Kelimeler

h-Stability, Time Scale, Alternative Variation of Parameters, Uniform Boundedness

Kaynakça

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