Buradasınız

Anasayfa » Content

SINIR ŞARTLARININ BİRİNDE ÖZDEĞER PARAMETRESİ BULUNDURAN SÜREKSİZ STURM-LİOUVİLLE PROBLEMİNİN ÖZFONKSİYONLARI

EIGENFUNCTIONS OF DISCONTINUOUS STURM-LIOUVILLE PROBLEM CONTAINING EIGENVALUE PARAMETER IN THE ONE OF BOUNDARY CONDITIONS

Journal Name:

  • Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi

Publication Year:

  • 2002

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper by using a new approach we investigate the resolvent operator and completeness of the system of eigenfunctions of the Sturm-Liouville problem with discontinuous coefficients and weight, one of the boundary conditions of which contained linear eigenparameter. For operator-theoretic formulation of the considered problem we define a new equvalent inner product in the Hilbert space L2[a,b] © C and suitable selfadjoint linear operator in it. Further, the basic solutions (|>(x, X) and %(x, X) are defined by the special procedure.
Bookmark/Search this post with
Abstract (Original Language): 
Bu çalışmada, sınır şartlarının birinin katsayıları özdeğer parametresini lineer olarak içeren süreksiz katsayılı ve ağırlıklı Sturm-Liouville probleminin rezolvent operatörü ve özfonksiyonlar sisteminin tamlık özellikleri yeni bir yaklaşımla incelenmiştir. İncelenen problemin operatör-teorik yazılımı için L2[a,b] © C Hilbert uzayında yeni eşdeğer iç çarpım ve uygun kendine eşlenik lineer operatör tanımlanmıştır. Ayrıca, ^(x, X) ve %(x, X) temel çözümleri özel bir yöntemle tanımlanmıştır.
FULL TEXT (PDF): 
PDF icon arastirmax-sinir-sartlarinin-birinde-ozdeger-parametresi-bulunduran-sureksiz-sturm-liouville-probleminin-ozfonksiyonlari.pdf
  • 2
219
226
  • Turkish

REFERENCES

References: 

Fulton, C. T. 1977. Two-point Boundary Value Problems With Eigenvalue Parameter Contained in the Boundary Conditions, England. Proc. Roy. Soc.
Edin. 77A, 293-308.
Glazman, J. M. 1965. Direct Methods of Qualitative Spectral Analysis. Jerusalem, Israel Program for Scientific Translations.
Lang, S. 1983. Real Analysis. Addison-Wesley, Reading, Mass.
Langer, R. E. 1932. A Problem in Diffusion or in the Flow of Heat For A Solid in Contact With A Fluid,
Japan. Tohoku Math. J. 35 , 360-375.
Mukhtarov, O, Sh and Demir, H. 1999.
Coerciveness of the Discontinuous Initial-Boundary Value Problem For Parabolic Equations, Israel. İsrael Journal of Mathematics 114 , 239-252.
Naimark, M. N. 1967. Linear Differential Operators. Ungar, New York,USA.
Rasulov, M. L. 1967. Methods of Contour Integration. North-Holland Pub. Comp. Amsterdam.
Taylor, A. E. 1958. Introduction to Functional Analysis. John Wiley.
Tikhonov, A. N and Samarskii, A. A. 1963. Equations of Mathematical Physics. Oxford and New York, Pergamon, USA.Titchmarsh, E. C. 1962. Eigenfunctions Expansion Associated With Second Order Differential Equations I 2nd edn, Oxford Univ. Press, London.
Titeux, I and Yakubov, Y. 1997. Completeness of Root Functions For Thermal Conduction in a Strip With Piecewise Continuous Coefficients. Mathematical Models and Methods in Applied
Sciences. Vol. 7, (7), 1035-1050.
Walter, J. 1973. Regular Eigenvalue Problems With Eigenvalue Parameter in the Boundary Conditions. Verlag. Math. Z. 133, 301-312.

Thank you for copying data from http://www.arastirmax.com