Taking into account the statement above: "What is the main conflict, or problem, concerns travis's inner maturation. When the fourteen-year-old is suddenly thrust into the role of head of the household, he has to deal with inner conflict, as well as outer conflict involving his household, wild animals, thieves, and hostile neighbors?"
Answer: Yeller becomes a surrogate father for Travis; the dog loves Travis unconditionally and a soul to whom Travis can confide his troubles.
Travis's climax is when Yeller gets rabies while fighting off a wolf. He knows that, for the good of his family, he has to shoot Yeller. This signifies his maturation, because is the main problem, on boy to man. At the end of the novel, Travis adopts one of Yeller's puppies from a neighbor's litter and, along with it, a new understanding of life, death, and the cycles of time.
Hope this helps.
