Sign properties of Green's functions for disconjugate dynamic equations on time scales. (Q1417978)

The author studies a two-point boundary value problem associated with the higher-order dynamic equation \[ y^{\Delta^n}+\sum_{i=1}^n q_i(t)\, \left( y^{\Delta^{n-i}} \right)^\sigma =0 \] on a time scale interval \([a,b]\). The author uses the concepts of a generalized zero (of order greater or equal to \(k\)), disconjugacy, and factorization to establish sign properties of the corresponding Green's functions. The results generalize and unify the corresponding continuous-time and discrete-time results. Anyone interested in the qualitative theory of differential, difference, and/or dynamic equations on time scales will find this paper useful.