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"existent literature" is correct and can be used in written English.
You can use it when you want to refer to the literature that exists, or has already been written. For example, "When researching this topic, one should look to the existent literature on the subject before coming to any conclusions."
Exact(24)
Thus, this paper has filled up a gap in the existent literature.
So, this paper filled up a gap in the existent literature.
Little effort has been made to integrate existent literature about prehospital temperature management.
We build on existent literature on technological change to frame the dynamics of how style changes across time.
The next section introduces a common framework encompassing the commodity and industry technology assumptions and also identifies the former as theoretically superior according to the existent literature.
According to our knowledge, in the existent literature, there are no input-output integral characterizations for uniform exponential trichotomy of skew-product flows.
Similar(36)
For vector-valued Gabor analysis, existent literatures mostly focus on L2 R,CL) instead of its subspace.
25 Research using randomised designs is non-existent, and literature on the subject remains scarce that is, firm evidence supporting or discouraging the use of ultraviolet B phototherapy at home is simply lacking.
These high values cannot satisfactorily be explained by the various models existent in the literature.
Here, a theoretical analysis indicates that the new equation is capable to generalize several models existent in the literature.
Through a meta-analysis, Blenker et al. (2014) found that almost half of the existent entrepreneurship education literature comes from UK.
Related(20)
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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