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

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 Dirichletintegrable solutions. Moreover we  share a relation between the kernel of the solution of the nonhomogeneous boundary value problem and the characteristic-matrix.