A continuous lower zone of a mafic rock called norite lies above a discontinuous zone of gabbro, some of which contains numerous broken fragments of the underlying basement rocks and some of which is rich in sulfide ore minerals of nickel, copper, and platinum-group metals.
The existence of a pair of well-ordered piecewise continuous lower and upper solutions implies the existence of a better pair of continuous lower and upper solutions.
One says that is a piecewise continuous lower solution of (1.1) if there exist such that.
Assume that all the conditions in Theorem 3.1 hold with piecewise continuous lower and upper solutions and.
Piecewise continuous lower and upper solutions in the sense of Definition 4.1 were already used in [15, 22].
Each varve is defined as a set of a continuous lower light (high-density) layer and upper dark (low-density) layer observed in the soft X-ray image.
Anyway, piecewise continuous lower and upper solutions are enough in practical situations, and since these can be transformed into continuous ones which provide better information we will only consider from now on continuous lower and upper solutions as defined in Definition 2.1.
In Section 4 we show that looking for piecewise continuous lower and upper solutions is good in practice, but once we have found them we can immediately construct a pair of continuous lower and upper solutions which provide better information on the location of the solutions.
It is possible to generalize further the concept of lower and upper solutions, as a piecewise continuous lower solution is a particular case of a bounded variation function that has a nonincreasing singular part.
As seen in many cases it is the long term effect that matters and continuous lower growth will in the long run add up to a substantial loss.
