Acta mathematica scientia,Series B ›› 2002, Vol. 22 ›› Issue (3): 335-345.

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ASYMPTOTIC BEHAVIOUR OF EIGENVALUES FOR THE DISCONTINUOUS BOUNDARY-VALUE PROBLEM WITH FUNCTIONALTRANSMISSION CONDITIONS

 O.Sh.Mukhtarov, Mustafa Kandemir   

  1. Department of Mathematics, Science and Arts Faculty, Gaziosmanpasa University, Tokat, Turkey

    Department of Mathematics, Faculty of Amasya Education, Ondokuz Mayis University, Amasya, Turkey
  • Online:2002-07-15 Published:2002-07-15
  • Supported by:

    The research was supported by TUBITAK.

Abstract:

In this study, the boundary-value problem with eigenvalue parameter gener-ated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and abstract linear functionals is investigated. So, the problem is not pure boundary-value.The authors single out a class of linear functionals and find simple algebraic conditions on
coefficients, which garantee the existence of infinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.

Key words: Asymptotic behaviour of eigenvalues, boundary-value problems, functional-conditions, discontinuous coefficients

CLC Number: 

  • 34L20
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