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Since is nondecreasing, this yields, for every, so.
Now, by and, it follows that for every there exists positive integer such that for every, so is a Cauchy sequence.
If then where for every So there exists such that for all.
from the definition of and the condition that then Thus, we get Similarly, we can prove that for every So the operator is well defined.
Therefore, for every so large, we have a lower and an upper solution to, respectively, such that (2.2) is satisfied and so, Corollary 2.5 guarantees that problem has at least one solution in the sense of distributions.
It follows at once from (3.3) that so that is decreasing along the flow lines and hence that maps into itself for every Also, if then for every so that by (iii).
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For every so-called imbalance on one side of the ocean, there exists an equal but opposite imbalance on the other side of the ocean.
Code Pink speaker and anti-war activist Cindy Sheehan, for example, raised the number of slain Pakistani civilians at the hands of drones even higher than the Pakistani claims when she stated (once again without ay proof or studies to back up her claim) that the CIA drone campaign "is by its own admission (sic) killing 100 or more innocent civilians for every so-called terrorist that they get.
They get together for dinners every so often.
Fortunately this never mattered for long; every so often something would bring us back to the theme.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com