Left-definite Hamiltonian systems and corresponding nested circles

Authors: EKİN UĞURLU

Abstract: This work aims to construct the Titchmarsh-Weyl $M(\lambda )-$theory for an even-dimensional left-definite Hamiltonian system. For this purpose, we introduce a suitable Lagrange formula and selfadjoint boundary conditions including the spectral parameter $\lambda $. Then we obtain circle equations having nesting properties. Using the intersection point belonging to all the circles we share a lower bound for the number of Dirichlet-integrable solutions of the system.

Keywords: Left-definite equations, Hamiltonian systems, Weyl's theory

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