## Green’s functions and comparison theorems for differential equations on measure chains.(English)Zbl 0938.34027

Summary: The authors are concerned with the selfadjoint equation $Lx(t)= [r(t) x^\Delta(t)]^\Delta+ q(t) x(\sigma(t))= 0.$ They study certain Green functions associated with this equation. Comparison theorems for initial value problems and boundary value problems are given.

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34B27 Green’s functions for ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations