There doesn’t appear to be anything ..
I clearly understand the "They don’t seem to be having difficulties", it is grammaticaly explainable, but the following:

"There doesn’t appear to be anything about generators"

1. What type of grammar this fall under .. and what are the rules? can I say ""There appear to be anything about generators"?
"
2. Do you know any examples of synonims of the "There doesn't appear to be"

ThanksSorry, here is the right one:

1. What type of grammar this fall under .. and what are the rules? can I say ""There appear to be a lot about generators"?

Question

There doesn’t appear to be anything ..
I clearly  understand the "They don’t seem to be having difficulties", it is grammaticaly explainable, but the following:

"There doesn’t appear to be anything about generators"

1. What type of grammar this fall under .. and what are the rules? can I say ""There appear to be anything about generators"?
"
2. Do you know any examples of synonims of the "There doesn't appear to be"

ThanksSorry, here is the right one:

1. What type of grammar this fall under .. and what are the rules? can I say ""There appear to be a lot about generators"?

Answer

We normally use "any..." for negative sentences and questions.

To make a positive sentence, you would use "There appearS to be a lot about generators ."

An equivalent of "There doesn't appear to be any..." would be "I don't see any..." or "I haven't found any..."

Answer

The verb "appear"   can be used as a linking verb to give the impression of being or doing something:
+ adjective 
She didn't appear at all surprised at the news.
It appears unlikely that interest rates will fall further.
+ noun 
He appears a perfectly normal person.appear to do something 
She appeared to be in her late thirties.
They appeared not to know what was happening.
There appears to have been a mistake.
it appears (that)… 
It appears that there has been a mistake.
It would appear that this was a major problem.