"in the existing literature" is correct and usable in written English. You can use it to refer to information or studies mentioned in previously written works. For example, "In the existing literature, it is suggested that people should limit their screen time to a few hours per day."
That is largely ignored in the existing literature.
The results are compared with those in the existing literature.
Their research revealed the lack of a broad view in the existing literature and anthologies.
There is no such attempt in the existing literature.
However, these issues remain unexplored in the existing literature.
A rigorous review has been done in the existing literature.
This study precisely address that gap in the existing literature.
However, it has not been studied in the existing literature.
Besides, in the existing literature, the tracking error is analyzed in the sense of λ-norm.
The obtained results unify, extend, and generalize some comparable results in the existing literature.
Our main results extend and improve some well-known results in the existing literature.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.