Birinci Dereceden Lineer Diferansiyel Denklemlerin Hyers-Ulam Kararlılığı
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2013
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Bu çalışmada öncelikle birinci mertebeden homojen ve homojen olmayan lineer adi diferansiyel denklemlerin Hyers-Ulam kararlılığı incelenmiştir. Daha sonra homojen olmayan birinci mertebeden lineer diferansiyel denklemlerin özel bir türünün Hyers-Ulam kararlılığı ispatlandı ve burada elde edilen sonuç ikinci mertebeden Cauchy-Euler denkleminin Hyers-Ulam kararlılığını göstermek için kullanılmıştır. Ayrıca lineer hale dönüştürülerek çözülebilen lineer olmayan birinci mertebeden adi diferansiyel denklemlerden Bernoulli ve Riccati diferansiyel denklemlerin Hyers-Ulam kararlılıkları ispatlanmıştır. Anahtar kelimeler: Lineer diferansiyel denklem, Hyers-Ulam kararlılığı, Cauchy-Euler denklemi, Bernoulli diferansiyel denklemi, Riccati diferansiyel denklemi.
In this paper, we firstly study the Hyers-Ulam stability of homogeneous and non-homogeneous linear differential equations of first order. Secondly we prove the Hyers-Ulam stability of a special kind of non-homogeneous linear differential equations of first order and then use the results obtained here to show the Hyers-Ulam stability of second order Cauchy-Euler equation. Also we prove the Hyers-Ulam stability of Bernoulli and Riccati differential equations that can be converted into a linear equation. Key words: Linear differential equation, Hyers-Ulam-Rassias stability, Cauchy-Euler equation, Bernoulli?s differential equation, Riccati differential equation.
In this paper, we firstly study the Hyers-Ulam stability of homogeneous and non-homogeneous linear differential equations of first order. Secondly we prove the Hyers-Ulam stability of a special kind of non-homogeneous linear differential equations of first order and then use the results obtained here to show the Hyers-Ulam stability of second order Cauchy-Euler equation. Also we prove the Hyers-Ulam stability of Bernoulli and Riccati differential equations that can be converted into a linear equation. Key words: Linear differential equation, Hyers-Ulam-Rassias stability, Cauchy-Euler equation, Bernoulli?s differential equation, Riccati differential equation.
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Matematik, Mathematics
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61