What it means
ようとしない follows the volitional form of a verb and means that someone does not try or make an effort to do something. It often suggests unwillingness, reluctance, or a repeated lack of effort, rather than simply stating that an action will not happen. The subject is usually a person or another intentional agent.
Usage note
ようとしない describes a refusal or failure to make an effort, so it is different from the ordinary negative form, which simply means that an action is not performed. It is normally used with verbs describing intentional actions.
How to use it
Verb (plain volitional form)としません
彼は難しい問題を解こうとしません。
He does not try to solve the difficult problem.
Verb (plain volitional form)としない
彼は難しい問題を解こうとしない。
He does not try to solve the difficult problem.