Is there a protagonist, and if so, is he static or dynamic in "Soldier's Home"?
Krebs is the protagonist and he is a dynamic character who has undergone change from his war experiences; he also shifts in his actions at the end of the story.
For the most part, the change in Krebs has taken place before most of the narrative as it is in the exposition that the reader learns how the war and Kreb's return home has affected him:
At first Krebs...did not want to talk about the war at all. Later he felt the need to talk but no one wanted to hear about it....Krebs found that to be listened to at all he had to lie, and after he had done this twice he, too, had a reaction against the war and against talking about it. A distaste for everything that had happened to him in the war set in because of the lies he had told.
Now, having returned to his home, Krebs cannot relate to his family or to the town in which nothing has changed. While the young girls have grown up, Krebs does not "feel the energy or the courage" to break into their circles....They were too complicated." So, at this point, Krebs seems to be stilted because he feels that "the world that they [the girls] were in was not the world he was in," and he takes no action since he feels detached from life in his hometown.
Further in the narrative when Krebs's mother talks with Krebs in her conventional manner, she urges him to "settle down to work" and maybe get married. Since Krebs says nothing, she asks him if he does not love her, and Krebs candidly replies, "No" because he cannot love anyone anymore. Because of his response, she is personally hurt in her lack of understanding of the void created in Krebs by his war experience. So, Krebs has to pretend he is her boy again and reaffirm his love for her. He even speaks as a child: "I know, Mummy....I'll try and be a good boy for you."
After she prays for Krebs, he leaves the house because he is sickened that he has lied to his mother, having "tried so to keep his life from being complicated." Thus, his mother becomes the catalyst of Krebs's shift to change again, a dynamic shift, as he resolves to move out of the house and go to Kansas City. "He wanted his life to go smoothly."