Quadratic functionals for second order matrix equations on time scales
Non-Linear Analysis
Sturm-Liouville eigenvalue problems on time scales
Applied Mathematics and Computation
Dynamic equations on time scales: a survey
Journal of Computational and Applied Mathematics - Dynamic equations on time scales
Higher-order self-adjoint boundary-value problems on time scales
Journal of Computational and Applied Mathematics
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In this work, we consider a linear Hamiltonian system x^@D=A"tx^@s + B"tu, u^@D=-C"tx^@s - A"t^Tu (H) on an arbitrary time scale @?, which allows one (among others) * to treat both continuous and discrete linear Hamiltonian systems (as the special cases for T=R and T=Z) within one theory; * to explain the discrepancies between these two theories while studying systems of form (H). As a main result, we prove that disconjugacy of system (H) is a sufficient condition for positive definiteness of the quadratic functional associated with (H), The principal tool is the Picone identity on @?. We derive also the corresponding Wronskian identity, Riccati equation in this general setting on time scales.