Irregular boundary value problems with discontinuous coefficients and the eigenvalue parameter

Mustafa Kandemir, Oktay Mukhtarov, Yakov Yakubov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this study, a Birkhoff-irregular boundary value problem for linear ordinary differential equations of the second order with discontinuous coefficients and the spectral parameter has been considered. Therefore, at the discontinuous point, two additional boundary conditions (called transmission conditions) have been added to the boundary conditions. The eigenvalue parameter is of the second degree in the differential equation and of the first degree in a boundary condition. The equation contains an abstract linear operator which is (usually) unbounded in the space Lq(-1, 1). Isomorphism and coerciveness with defects 1 and 2 are proved for this problem. The case of the biharmonic equation is also studied.

Original languageEnglish
Pages (from-to)317-338
Number of pages22
JournalMediterranean Journal of Mathematics
Issue number3
StatePublished - Oct 2009


  • Boundary value problem
  • Coerciveness
  • Discontinuous coefficient
  • Eigenvalue parameter
  • Isomorphism
  • Problem with a defect
  • Transmission conditions


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