Summary: We establish the analogues of classical Sturmian theorems (comparison theorem, oscillation theorem, zeros-separation theorem) for linear difference equations (and inequalities) with continuous time (DECT)
As a result we obtain:
(a) Sharp conditions for the oscillation of all solutions of the above equation (with and ) in terms of its coefficients;
(b) Upper estimates (and some lower estimates as well) for the length of the sign-preservation intervals for solutions;
(c) Some properties for the DECTs with no regular oscillatory solutions.