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and strongly order preserving if (2.5).
If T is strongly order preserving, then there exists a fixed point in ([!![a,b ]!!]) which is stable relative to ([!![a,b ]!!]).
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We talk about the series that she loves – The Sopranos, The Wire, Breaking Bad – and an article she once read that explored "our fascination with these very strongly ordered patriarchal communities".
The intriguing fact that no domains at all are formed during the recrystallization of strongly ordered intermetallics such as Ni3Al is discussed and a reason is proposed.
Under, is satisfied, and is strongly order-preserving.
We know that is strongly order-preserving, so does given in Lemma 2.1.
Since the right-hand side of (4.7) defines a compact strongly order-preserving operator, we find that ϕ must change sign in ( p, q ).
Lemma 3.2 (see [20]). is a linear completely continuous operator and also a linear completely continuous operator from In addition, is strongly order-preserving.
If there exist no strict supsolution and supersolution required in [20], just only using the functional to get the critical point [10, 11], then we just know that (BVP) (1.2) has solutions, even we can know the sign of the critical point of the functional because is not strongly order-preserving in.
Then ((mathbb{Y},mathbb{Y}^)) is a strongly ordered Banach space.
Define (X^=C overline{Omega}, mathbb{R}_^{2})); then ((X,X^)) is a strongly ordered space.
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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