On the characteristic functions and Dirchlet-integrable solutions of singular left-definite Hamiltonian systems

Bayram E., Taş K., Uğurlu E.

Quaestiones Mathematicae, vol.47, no.5, pp.983-995, 2024 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 5
  • Publication Date: 2024
  • Doi Number: 10.2989/16073606.2023.2277841
  • Journal Name: Quaestiones Mathematicae
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.983-995
  • Keywords: Dirichlet-integrable solutions, Hamiltonian systems, Left-definite equations
  • Uşak University Affiliated: Yes

Abstract

In this work, a singular left-definite Hamiltonian system is considered and the characteristic-matrix theory for this Hamiltonian system is constructed. Using the results of this theory we introduce a lower bound for the number of Dirichlet-integrable solutions. Moreover we share a relation between the kernel of the solution of the nonhomogeneous boundary value problem and the characteristic-matrix.