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

Erbe, Lynn; Peterson, Allan

Dyn. Contin. Discrete Impulsive Syst. 6, No. 1, 121-137 (1999).

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

Keywords:

differential equations on measure chains; Green functions; initial value problems; boundary value problems