There are a couple of major conflicts threaded throughout this novel, which is an unexpectedly lovely story, humorous and heartbreaking, of two boys struggling with very different--but in some ways similar--problems. Kevin is intellectually gifted, but physically handicapped, and experiences all the frustration that comes with being different, especially when one is a young person. Max is a good sized kid, physically intimidating perhaps, but he's always struggled a great deal in school. So these two young men are both struggling with "person versus self" conflicts as they try to make sense of, and deal with their respective weaknesses in a world that does not necessarily view either of them with great sensitivity.
As the two boys become friends, they find respite in each other's strengths. Kevin can get around quickly, and with a great view, because Max carries him around on his shoulders; Max learns, through Kevin, to use his imagination and not be afraid to think, specifically, to not be afraid that his thoughs are inadequate because of his intellectual struggles. Kevin gives Max plenty of advice and instructions during their time together including this commentary:
Matter of fact, I watch tons of tube, but I also read tons of books so I can figure out what's true and what's fake, which isn't always easy. Books are like truth serum--if you don't read, you can't figure out what's real.
Although Kevin's physical conflict ends with his death, he literally and figuratively gives Max his life back: literally, because when Max's convict father is holding Max hostage, Kevin shows up and squirts Kenny's eyes with what he says is a poisonous chemical compound, but is in fact soap and curry powder, thus allowing Max to escape, and figuratively as his time with Kevin becomes a catalyst for Max to begin to write creatively, in order to tell their story after Kevin's death.