Research Article

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

Published in: Quaestiones Mathematicae
Volume 47 , issue 5 , 2024 , pages: 983–995

DOI: 10.2989/16073606.2023.2277841

Author(s): Elgiz Bairamov Ankara University, Turkey , Kenan Tas Usak University, Turkey , Ekin Uğurlu Çankaya University, Turkey

Keywords: Primary: 34B20 , 37J35 , Secondary: 15A60 , Left-definite equations , Hamiltonian systems , Dirichlet-integrable solutions

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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.

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