Turkish Journal of Mathematics
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.
Left-definite equations, Hamiltonian systems, Weyl's theory
"Left-definite Hamiltonian systems and corresponding nested circles,"
Turkish Journal of Mathematics: Vol. 47:
4, Article 17.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss4/17