Oscillation results for a dynamic equation on a time scale. (English) Zbl 1002.39024

Akin, Elvan; Erbe, Lynn; Peterson, Allan; Kaymakçalan, Billur

J. Difference Equ. Appl. 7, No. 6, 793-810 (2001).

Authors’ abstract: First we are concerned with properties of an exponential function for a dynamic equation on a time scale. We completely determine the sign of this exponential function. This then determines when first order linear homogeneous dynamic equations and their adjoints are oscillatory or nonoscillatory. In the last section of this paper we give oscillation criterion for a certain higher order linear dynamic equation on a time scale.

Reviewer: Sui Sun Cheng (Hsinchu)

MSC:

39A11	Stability of difference equations (MSC2000)
39A10	Additive difference equations

Keywords:

measure chains; time scales; oscillation; exponential function; dynamic equations