Square dA-integrable solutions of differential systems with measures on the semiaxis

Authors

  • Viktor Mazurenko Vasyl Stefanyk Precarpathian National University, Ukraine
  • Oles Mazurenko Ivan Franko National University of Lviv, Lviv, Ukraine

DOI:

https://doi.org/10.31471/2304-7399-2023-18(68)-32-48

Keywords:

differential system with measures, Green's matrix, characteristic matrix, Weyl--Titchmarsh theory, matrix limiting disk, square $dA$-integrable solution

Abstract

This paper extends the Weyl-Titchmarsh theory to the case of generalized differential systems. It is that proved the characteristic matrix of the resolvent kernel of a differential system with measures belongs to a locus, which is a matrix analog of the Weyl disk. It is established that such matrix disks are nested and converge to the limiting disk or point depending on the limiting behavior of the radii. This limiting set plays an important role in discussing of the number of solutions to such system that are square dA-integrated on the semiaxis.

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Published

2023-12-01

How to Cite

Mazurenko, V., & Mazurenko, O. (2023). Square dA-integrable solutions of differential systems with measures on the semiaxis. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY Number, (18(68), 32–48. https://doi.org/10.31471/2304-7399-2023-18(68)-32-48