What is the function of the に in 差別化に大変?


アトラクション要素として、店内にメリーゴーランドでも設置したのだろう。場末の居酒屋は他店との差別化 **に**
大変なんだろうな。その経営努力、わからんでもない。

Hi. I know the underlined sentence means "Differentiating their izakaya
restaurant from others is difficult.". And some say the bold に is a mistake,
which should be が. Some say the に is a colloquialism to use -ni to introduce
the aim of an endeavor for 大変だ, as in "最初はすごく理解されるのに大変だったけれど、"(I don't quite
understand this explanation).

Could you please shed some light on the function of this に? Personally I don't
really think it is a mistake, but I can't find this usage in my textbook
ether.

Thank you.




If I had to choose [a
definition](https://dictionary.goo.ne.jp/word/%E3%81%AB/#jn-166083) from a
dictionary, it'd be this:

> **５** 動作・作用の目的を表す。「見舞いに行く」「迎えに行く」

But it is far from enough specific for your question, I guess.

The explanation you got "to introduce the aim of an endeavor" is basically
correct, that the expression implies that someone is _doing_ something at the
moment, and tells what condition they are in (by adjective), trying to achieve
or finish what (by に).

> 先生はテストの採点に忙しい _The teacher is busy marking the tests._  
>  監督は決定力の強化に熱心だ _The manager is eager in improving scoring ability._

The adjective has to describe a certain manner of an action, so "action-less"
kind of words like mental adjectives are not allowed.

> × 私は日本語の勉強に面白い

> 場末の居酒屋は他店との差別化に大変なんだろうな。  
>  "I guess an izakaya in an outlying area must be desperate for
> differentiating itself from others."  
>  "I guess an izakaya in an outlying area must try the hard way to
> differentiate itself from others."  
>  "I guess an izakaya in an outlying area always struggles to differentiate
> itself from others."




If I had to choose [a
definition](https://dictionary.goo.ne.jp/word/%E3%81%AB/#jn-166083) from a
dictionary, it'd be this:

> **５** 動作・作用の目的を表す。「見舞いに行く」「迎えに行く」

But it is far from enough specific for your question, I guess.

The explanation you got "to introduce the aim of an endeavor" is basically
correct, that the expression implies that someone is _doing_ something at the
moment, and tells what condition they are in (by adjective), trying to achieve
or finish what (by に).

> 先生はテストの採点に忙しい _The teacher is busy marking the tests._  
>  監督は決定力の強化に熱心だ _The manager is eager in improving scoring ability._

The adjective has to describe a certain manner of an action, so "action-less"
kind of words like mental adjectives are not allowed.

> × 私は日本語の勉強に面白い

> 場末の居酒屋は他店との差別化に大変なんだろうな。  
>  "I guess an izakaya in an outlying area must be desperate for
> differentiating itself from others."  
>  "I guess an izakaya in an outlying area must try the hard way to
> differentiate itself from others."  
>  "I guess an izakaya in an outlying area always struggles to differentiate
> itself from others."

