Nonlocal boundary-value for abstract second-order differential equation with operator involution.

Authors

  • Yu.O. Baranetskij Lviv Polytechnic National University
  • P.I. Kalenyuk Lviv Polytechnic National University, University of Rzeszow
  • L.I. Kolyasa Lviv Polytechnic National University

Keywords:

differential-operator equation, root function, operator of involution, essentially a nonself-adjoint operator, Riesz basis, nonlocal problem

Abstract

We study a nonlocal problem with generalized conditions Ionkin's for the Sturm-Liouville equation with polynomial potential which contains an involution operator. The spectral properties of the operator of this problem are analyzed and the conditions for the existence and uniqueness of its solution are established. It is also proved that the system of root functions essentially a nonself-adjoint operator of the analyzed problem forms a Riesz basis.

Author Biographies

Yu.O. Baranetskij, Lviv Polytechnic National University

Doctor of Philosophy, associate professor department of mathematics

P.I. Kalenyuk, Lviv Polytechnic National University, University of Rzeszow

Doctor of Science, professor department of mathematics

L.I. Kolyasa, Lviv Polytechnic National University

Doctor of Philosophy, senior lecturer department of mathematics

Downloads

Issue

No. 1/2 (2016)

Section

Mathematics