Standart olmayan büyüme koşullu eliptik denklemlerin çözümlerinin varyasyonel yaklaşım altında incelenmesi
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Tarih
2015
Yazarlar
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Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
İlk bölümde üzerinde çalışılan uzayın gelişimi ve literatür hakkında bilgi verilmiştir. İkinci bölümde çalışma boyunca ihtiyaç duyulan temel kavram, tanım ve teoremlerden söz edilmiş, Lebesgue ve Sobolev uzayları hakkında bilgi verilmiştir. Üçüncü bölümde varyasyonel yaklaşım ve varyasyonel yaklaşımla ilgili temel kavram, tanım ve teoremlerden söz edilmiş, ayrıca varyasyonel yaklaşımın uygulandığı bazı problem türlerinden bahsedilmiştir. Dördüncü bölümde eliptik bir denklem sistemi varyasyonel yaklaşımla incelenerek, sıfırdan farklı çözümler Mountain-Pass Teoremi ve Cerami koşulu kullanılarak elde edilmiştir. Beşinci bölümde Kirchhoff problemi varyasyonel yaklaşımla incelenerek, sıfırdan farklı çözümler Krasnoselskii Genus Teoremi ve Palais-Smale koşulu yardımıyla elde edilmiştir.
In the first chapter, the necessary knowledge about development of the space and literature are given. In the second chapter, some basic definitions and theorems are given which are the necessary for properly understanding of the following chapters. Moreover, the Lebesgue and Sobolev space are mentioned. In the third chapter, variational approach and the related basic concepts, definitions and theorems are given. Furthermore, applications of variational approach to the some problem types are given. In the fourth chapter, in view of variational approach, by using Mountain Pass Theorem and Cerami condition the the existence of nontrivial solutions of an elliptic system are obtained. In the fifth chapter, in view of variational approach, by using Krasnoselskii?s Genus Theorem and Palais-Smale condition the the existence of nontrivial solutions of a Kirchhoff equation are obtained.
In the first chapter, the necessary knowledge about development of the space and literature are given. In the second chapter, some basic definitions and theorems are given which are the necessary for properly understanding of the following chapters. Moreover, the Lebesgue and Sobolev space are mentioned. In the third chapter, variational approach and the related basic concepts, definitions and theorems are given. Furthermore, applications of variational approach to the some problem types are given. In the fourth chapter, in view of variational approach, by using Mountain Pass Theorem and Cerami condition the the existence of nontrivial solutions of an elliptic system are obtained. In the fifth chapter, in view of variational approach, by using Krasnoselskii?s Genus Theorem and Palais-Smale condition the the existence of nontrivial solutions of a Kirchhoff equation are obtained.
Açıklama
Anahtar Kelimeler
Matematik, Mathematics, Lebesgue ve Sobolev Uzayları, Varyasyonel Yaklaşım, Standart Olmayan Büyüme Koşulu, Mountain-Pass Teoremi, Krasnoselskii Genus Teoremi, Cerami Koşulu, Palais-Smale Koşulu, Lebesgue and Sobolev Spaces, Variational Approach, Nonstandar Growth, Condition, Mountain-Pass Theorem, Krasnoselskii’s Genus Theorem, Cerami Condition, PalaisSmale condition
