Heriot-Watt Mathematics Report Series
HWM06-16, 21 Apr 2006

The formulation of second order boundary value problems on time scales

F A Davidson and B P Rynne


Abstract

In this paper we reconsider the basic formulation of

second order, two-point, Sturm-Liouville-type boundary value problems

on time scales.

Although this topic has received extensive attention

in recent years, we present some simple examples which show that

there are certain difficulties with the formulation of the

problem as usually used in the literature.

These difficulties can be avoided by some additional conditions on

the structure of the time scale, but we show that these are

unnecessary, since in fact a simple,

amended formulation of the problem avoids the difficulties.

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