Nonlocal multipoint problem for a differential equation of $2n$-th order with operator coefficients

  • Ya.O. Baranetskij Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine
  • I.I. Demkiv Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine
  • A.V. Solomko Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-6213-4130
  • O.M. Sus' Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
Keywords: multipoint problem, antiperiodic boundary condition, root function, method of transmutation operators, Riesz basis
Published online: 2021-10-29

Abstract


In the article, the spectral properties of a multipoint problem for a differential operator equation of order $2n$ are studied. The operator of the problem has an infinite number of multiple eigenvalues. Each multiple eigenvalue corresponds to a finite set of root functions. A commutative group of transmutation operators is constructed. Each element of the group corresponds to the isospectral perturbation of the problem operator with antiperiodic conditions. The conditions for the existence and uniqueness of the solution are established for the selected family of multipoint problems, and this solution is constructed too.

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How to Cite
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BaranetskijY.; DemkivI.; SolomkoA.; Sus’O. Nonlocal Multipoint Problem for a Differential Equation of $2n$-Th Order With Operator Coefficients. Carpathian Math. Publ. 2021, 13, 501-514.

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