How is the main problem resolved in Catching Fire?

The one of the main conflicts in Catching Fire is an internal conflict, as Katniss determines whether or not she wants to be a part of the growing rebellion against The Capital. It is interesting that, for such an active character, this decision gets made for Katniss, instead of her making it for herself. At the beginning of the novel, President Snow threatens her, saying that uprisings may be coming if she doesn't fall in line and convince the people in the districts that love, not rebellion, motivated her bluff of committing suicide with the poisoned berries in The Hunger Games. At the time, Katniss says that she is "both chilled and somewhat elated by the possibility" (Chapter 2). 

In District 11, she seems to encourage rebellion again, by speaking from the heart about Rue. However, this is accidental; her goal was to share with Rue's family, but her actions and words have consequences for the people of District 11, as the man who whistled Rue's signal is executed. Again, Katniss vows to squash rebellion for peoples' safety, even though she would love for The Capital to be overthrown.

After the Victor's Tour, Gale encourages Katniss to be the face of the rebellion and again she refuses, claiming that she can't be responsible for so many people getting hurt in what she sees as a lost cause. However, when Katniss meets Twill and Bonnie and hears about their journey towards District 13, she begins to hope that rebellion may be possible.   

Once Katniss realizes she will have to go back into the Games, however, all thoughts of rebellion are driven from her mind. However, Haymitch continues working, using his knowledge of Peeta and Katniss and their relationship to manipulate them into working with the other Victors in the arena, who are in on the plot. In the end, Katniss is rescued from the arena by District 13 and the rebels. In this way, the conflict of whether Katniss will joint he rebellion or not is decided for her. Still, in Mockingjay, she will continue to struggle with how much cooperation she will provide to the rebel forces, so the conflict is not entirely resolved.