The nonlocal boundary value problem with perturbations of mixed boundary conditions for an elliptic equation with constant coefficients. II

  • Ya.O. Baranetskij Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine
  • P.I. Kalenyuk Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine https://orcid.org/0000-0003-3456-9185
  • M.I. Kopach Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • A.V. Solomko Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
Keywords: differential equation with partial derivatives, root functions, Fourier method, method of transform operators, Riesz basis
Published online: 2020-06-28

Abstract


In this paper we continue to investigate the properties of the problem with nonlocal conditions, which are multipoint perturbations of mixed boundary conditions, started in the first part. In particular, we construct a generalized transform operator, which maps the solutions of the self-adjoint boundary-value problem with mixed boundary conditions to the solutions of the investigated multipoint problem. The system of root functions $V(L)$ of operator $L$ for multipoint problem is constructed. The conditions under which the system $V(L)$ is complete and minimal, and the conditions under which it is the Riesz basis are determined. In the case of an elliptic equation the conditions of existence and uniqueness of the solution for the problem are established.

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How to Cite
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Baranetskij Y., Kalenyuk P., Kopach M., Solomko A. The Nonlocal Boundary Value Problem With Perturbations of Mixed Boundary Conditions for an Elliptic Equation With Constant Coefficients. II. Carpathian Math. Publ. 2020, 12 (1), 173-188.

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