In a research paper comparing Speak (Anderson) and Hamlet (Shakespeare) you could examine the ways which Speak can be paralleled to the Elizabethan revenge play of Hamlet. Given that Hamlet is a play which depicts "a corrupt act, the killing of a king, undermines order throughout the realm that resonates to high heaven," Speak does this as well.
In Speak, readers see a corrupt act (the rape and subsequent alienating of Melinda) the "killing of a king" (figuratively, in the death of Melinda's confidence, friendships, and self-identity), and the undermining of order (as seen in the friendships which dissolve because of Melinda calling the cops at the party where she was raped).
While stretching the parallels, which is what a research paper does, this comparison will allow contemporary fiction to be tied to historical fiction--a tie which should be regarded as worthy of "reward."
A very rewarding research paper topic that you can use with "Speak" by Laurie Halse Anderson and "Hamlet" by Shakespeare is to investigate the similarities and differences between Melinda's secret that she carries that she was raped and how it influences her behavior and development throughout the novel and Hamlet's secret in the fact that he knows that his father was murdered by his uncle.
How do those two main protagonists of their respective works of literature deal with their secrets and what are the eventual outcomes of dealing with those secrets. Do the frie4nds of Melinda in "Speak" know her secret and do the friends of Hamlet know his secret? Do they both deal with that knowledge in similar or different ways? Do their secrets interfere with their personal relationships and how does each character deal with the underlying weight of understanding the eventual outcomes of what their secrets do to their own personal behavior? Is a secret a positive thing or a negative thing for each character? Can some good come out of their knowledge of their secrets?
These might be very interesting questions that can be answered in a very thoughtful research paper in three to five pages. I hope you find the assignment very rewarding.