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"You're caught between 'I want the dues paid' and 'I want a peaceable, nice existence,' " Ms. Aikens said.
Using some fixed point theorems, they obtained some nice existence conditions for positive solutions.
As long as the Banach space is reflexive, the weak compactness offers no problem since every bounded subset is relatively weakly compact and therefore the weak continuity suffices to prove nice existence results for differential and integral equations [1, 2].
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As Morgan put it, "All I'm interested in is settling down to a nice, peaceful existence".
Indeed, we have successfully adapted the proof of Theorem 4.4 to readily get a nice analogous existence result for x ′ = f ( t, x ), t ∈ [ 0, 1 ], x ( 0 ) = x 0 ∈ R, but we have decided not to include it here because it was just a particular case to [8], Theorem 2.4] (although easier to prove).
Can existence not exist?
Still, it's just nice to forget about the existence of Silent Witness for an hour and let the TV shout – actually, whisper – boo to your mind.
There's also a games room and, in a nice nod to its former existence, some old fashioned school desks that are perfect for doing jigsaws, drawing or – perhaps more likely – figuring out who owes the kitty what for all the local wine consumed.
Therefore it is quite difficult to expect any nice behavior that will imply the existence of a fixed point.
Therefore it is quite difficult to expect any nice behavior that will imply the existence of a fixed point for this class of mappings.
Describing Flory's own feelings about his cross-genre career, Associated Press writer Jay Sharbutt wrote that "Med, who speaks in an easy Indiana drawl, doesn't mind this split-ticket existence: 'It makes a nice balance in life,' he says.
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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