"At least one" clause in Relational Algebra
A first hint toward a solution is to think about "what's the result of a natural join between $Author$, $Publication$ and $AuthorPublication$?" 
The answer is "the universal relation" $R(BookID,AuthorID,Title,Year,Name)$ describing who wrote a book and when. Note that a book without any author or an author without any book written won't appear in $R$. So an author in $R$ as written at least one book. The following query gives the authors who wrote at least a book in year 2008:
$$ \pi_{Name}(Author \Join AuthorPublication \Join \sigma_{(2008 =  year)}(Publication))$$

For the final answer, compute the intersection of this query with its variants:
$$ \pi_{Name}(Author \Join AuthorPublication \Join \sigma_{(2008 =  year)}(Publication)) \cap \pi_{Name}(Author \Join AuthorPublication \Join \sigma_{(2009 =  year)}(Publication)) \cap \pi_{Name}(Author \Join AuthorPublication \Join \sigma_{(2010 =  year)}(Publication))$$

You may provide other equivalent answers with outer $Author \Join$.