By "problem novel" I assume you mean a novel that talks about a social problem. Therefore, I will choose<em> Uncle Tom's Cabin</em> as an example, as it dealt with the problem of slavery.
The novel has several settings. It begins in Kentucky, where we meet the Shelby family. They are slave owners, and they find themselves in a difficult financial situation. In order to solve it, they decide to sell two slaves: Tom, a loyal, deeply religious middle-aged man, and Harry, the son of a young slave called Eliza. Eliza decides to escape, and Tom decides to stay, and the novel follows the two of them.
Eliza is successful in her escape. She is aided by Quakers and eventually arrives with her son and husband to Canada. Tom is not so lucky. He is sold to a plantation in the South. He is happy there, and his owner appreciates him. However, the owner dies and Tom is sold to another plantation owner called Legree. He is abusive and ends up killing Tom.
The novel was written with the purpose of bringing the reality of slavery to more people. It tried to persuade people of how wrong and inhumane this practice was. It was a significant and influential novel in the abolitionist movement.
