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The phrase "under certain conditions" is correct and usable in written English
You can use it when referring to a set of specific, usually restrictive, conditions that must be satisfied for something to be possible. For example, "I will accept your offer of marriage under certain conditions."
Exact(35)
The jumping phenomenon clearly occurs under certain condition.
It is proved that under certain condition there always exists an optimal ordering that respects modules.
Boiling water reactors are susceptible to instabilities under certain condition and require stability boundary to prevent instability.
Our finding that α-Al2O3 nucleates under certain condition provides a solid basis to elaborate condensation models of dust around oxygen-rich evolved stars.
It is then shown that, under certain condition, optimal smoothing splines converge to this curve as the number of data increases.
It is also found that softer foams with low stiffness are more effective as shock absorbing cushion against ballistic impacts under certain condition.
Similar(25)
My answer is yes — under certain conditions.
Yes, of course, but only under certain conditions.
"The federation should sell the rights under certain conditions.
It will probably be granted, he said, under certain conditions.
Disadvantages can become advantages only under certain conditions.
More suggestions(15)
under specified condition
under given condition
under certain terms
under certain requirements
under selected condition
under certain conditions
at certain condition
in certain condition
under specific condition
under some condition
under cold condition
under certain criteria
under hypoxic condition
under such condition
under particular condition
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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