TY - JOUR T1 - On Coincidence Degree Theory Some Corrections and Explanations TT - Örtüşen Derece Teorisi Üzerine Bazı Düzeltme ve İzahlar AU - Sırma, Ali PY - 2019 DA - March JF - Haliç Üniversitesi Fen Bilimleri Dergisi JO - Temel Bilimler Genel PB - Halic University WT - DergiPark SN - 2618-6241 SP - 17 EP - 34 VL - 2 IS - 1 LA - en AB - Coincidence degree theory, also known Mawhin’s coincidence theory is very powerful technique especially in existence of solutions problems in nonlinear equations. It has especially so broad applications in the existence of periodic solutions of nonlinear differential equations so that many researchers have used it for their investigations. In coincidence degree, mainly existence of solutions of the operator equation in the form in an open and bounded set in some Banach space was researched. Here, is a linear operator and is a nonlinear operator satisfying some special properties. In this study mainly the studies of Gaines and Mahwin are followed, the statement of continuation theory in a coincidence degree theory was corrected and the reason is expressed. A continuation theorem was expressed in different manner. In order to help the researchers with their studies on this subject, the proof that was provided by Gaines and Mawhin has now been presented with more detailed explanation. KW - Coincidence Degree Theory KW - -compact operator KW - Homotopy Theory N2 - Gaines-Mawhinörtüşen derece teorisi olarak da bilinen örtüşen derece teorisi, özellikledoğrusal olmayan denklemlerdeki çözümün varlığı probleminde güçlü birtekniktir. Özellikle doğrusal olmayan differensiyel denklemlerin periyodikçözümlerinin varlığının gösterilmesinde çok geniş bir uygulaması olduğundan pekçok araştırması çalışmalarında bu metodu kullanmışlardır. Örtüşen dereceteorisinde, bir Banach uzayındaki açık ve sınırlı kümesinde tanımlı formundaki bir operatör denklemininçözümlerinin varlığı araştırılır. Burada bir doğrusal operatör ve doğrusal olmayan bir operatör olmak üzere ve bazı özel koşulları sağlayan operatörlerdir.Bu çalışmada esas olarak Gaines ve Mawhin’in çalışmaları takip edilmiş, örtüşen teorininsürdürülebilirlik teoreminin ifadesindeki ikinci sonuç düzeltilmiş ve gerekçesibelirtilmiş. Her ne kadar uygulamalarda birinci sonuç kullanılsa da buikincisinin düzeltilmesi de önemli bir çalışmadır. Bu sürdürülebilirlikteoreminin farklı bir şekilde ifadesi verilmiş. Gaines ve Mawhin’in çok azizahla verdiği ispat ilerideki çalışmalara bir yardımcı olmak amacıylayeterince detaylı bir şekilde izah edilmeye çalışılmıştır. CR - [1] Gaines, R. E., and Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations, vol. 568 of Lecture Notes in Mathematics, Springer, 1977. 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