Can I ask an author to send me his ebook?
Certainly you can ask. There is nothing wrong with that. If you explain a bit about your use and the restrictions you face it might make it more likely that the author might try to help you. 

But the author might not be able to comply with your request due to contractual arrangements with the publisher (if any). So, you might get a reply that starts out "Sorry, but..."

On the other hand, I'm surprised that libraries don't have access. I would guess that if you take your request to the librarian him/herself, you might learn that copies of nearly everything can be borrowed. Librarians have a vast, legal, network of sources for academic/scientific works. Even my town library, which has no formal relationships, can find just about anything I need, though the sources are usually all in this country. 

But there are no ethical issues about asking. Etiquette only requires politeness and being honest about your needs.