Abstract
Working with general linear Hamiltonian systems on [0, 1], and with a wide range of self-adjoint boundary conditions, including both separated and coupled, we develop a general framework for relating the Maslov index to spectral counts. Our approach is illustrated with applications to Schrödinger systems on \({\mathbb {R}}\) with periodic coefficients, and to Euler–Bernoulli systems in the same context.
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Acknowledgements
Research of S. Jung was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1C1B1009978). Research of B. Kwon was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2015R1C1A1A02037662). This collaboration was made possible by P. Howard’s visit to Ulsan National Institute for Science and Technology in July 2016, and by S. Jung’s and B. Kwon’s visits to Texas A&M University in July 2017. The authors acknowledge the National Research Foundation of Korea for supporting these trips.
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Howard, P., Jung, S. & Kwon, B. The Maslov Index and Spectral Counts for Linear Hamiltonian Systems on [0, 1]. J Dyn Diff Equat 30, 1703–1729 (2018). https://doi.org/10.1007/s10884-017-9625-z
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DOI: https://doi.org/10.1007/s10884-017-9625-z