Do I need to add the in front of reluctance? Is the use of others right?
The problem that this study addresses is that the reluctance of newly educated nurses to make their careers in hospitals causes the shortage of nurses. Others have done about the problem the researcher has identified. Hassmiller (2006) performed a regression analysis to determine whether reluctance of nurses to make their careers in hospitals caused the shortage of nurses.
'the' has been used to restrict the meaning of the noun, reluctance. To make it refer to something that is known by both the speaker or writer and the listener or reader.
First, use of an article in this case is not required. "The problem that this study addresses is that reluctance of newly educated nurses to make their careers in hospitals causes a shortage of nurses" is acceptable.
At the same time, using an article before "reluctance" is also acceptable.
If the concept of "reluctance" has already been introduced and the study is returning to that concept, then it is appropriate to say "the reluctance". For instance:
Studies have found that over 80% of newly educated nurses are reluctant to make their careers in hospitals. This contrasts with only 10% fifty years ago. Studies have also found that there is currently a 50% shortage of nurses in US hospitals. This contrasts with a 3% shortage fifty years ago. The problem that this study addresses is that the reluctance of newly educated nurses to make their careers in hospitals causes the shortage of nurses.
In the example of above it is appropriate to say "the reluctance" and "the shortage" because both of these concepts have already been introduced and thus become specific.
It would also be appropriate to use the article "the" with something that is self-defined, such as "the study" (clearly the study referred to in your question), "the Holy Grail" (there's only one), "the article 'a'" (there's only one article 'a' in English), "the first sentence of the study" (there can only be one first sentence of the study). Because it is specific and self-defined, I think that "the reluctance of newly educated nurses to make their careers in hospitals..." would be acceptable even if it was used in the first sentence of the study, and not previously defined. However, I cannot say the same thing about "shortage of nurses" - this is too vague, because it's possible that there could be more than one shortage of nurses, so it's not really specific enough to use "the" if it wasn't previously defined. Therefore, if it was used in the first sentence of the study, and not previously defined, then it would be better to use the article "a" instead of "the" to preceed "shortage of nurses". For instance:
The problem that this study addresses is that the reluctance of newly educated nurses to make their careers in hospitals causes a shortage of nurses. This study finds that 80% of newly educated nurses are reluctant to make their careers in hospitals, contrasting with only 10% fifty years ago. At the same time, there is currently a 50% shortage of nurses in US hospitals, contrasting with a 3% shortage fifty years ago. This study further demonstates that these two items are directly correlated.
In the example above, because the concept of shortage has not been previously introduced in the study, and because there could potentially be multiple shortages of nurses, it is preferable to use the article "a" not "the" with "shortage", but with "relucance", because it's so specifically defined, the use of "the" is fine.
