Spectral Analysis of ˛-Semi Periodic 2-Interval Sturm-Liouville Problems

• O Sh. Mukhtarov ^[2] ; K. Aydemir ^[1]
  1. [1] Amasya University

     Amasya University

     Turquía

     
  2. [2] Gaziosmanpa¸sa University & Azerbaijan National Academy of Sciences
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • In this paper, we propose a new type of boundary value problems for 2-interval SturmLiouville equations which differs from the classical periodic Sturm-Liouville problems in that, the boundary and transmission conditions depend on a positive parameter α > 0. We will call this problem α-semi periodic Sturm-Liouville problem. It is important to note that our problem is not self-adjoint in the classical Hilbert space of squareintegrable functions L2[−π, π] when the parameter α = 1. First by using an our own approach we investigated some properties of eigenvalues and their corresponding eigenfunctions. Then, for self-adjoint realization of the problem under consideration we define a different inner product in the classical Hilbert space in which we treated an operator-theoretic formulation. The results obtained generalize and extend similar results of the classical periodic Sturm-Liouville theory, since in the special case α = 1 our problem is transformed into classical periodic Sturm-Liouville problems.

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