Some Applications of the Boundary-Locus Method and the Method of D-Partitions

We summarize aspects of the method of D-partitions and its analogue,the boundary-locus technique. We apply these techniques to adiscussion of the stability of the delay equation where y(t)=(t), t –, 0]. Some comparisons with resultsvalid for other functional equations are introduced. Of interestare the following features: (i) the results corresponding toour results but applicable to delay-differential equations arenot found in the literature, (ii) some unconventional parameterspaces are introduced, and (iii) the possibility of extendingresults which hold for a basic test equation to more generalequations is established.