In Hatchet there are many "problems", otherwise known as conflicts.  Usually when writing about literature we say "conflict" when talking about problems characters encounter.  Conflicts can be internal, and Brian certainly has plenty of those, even before he gets stranded.  They can also be external, such as a conflict with another person, an animal, or with nature.  Brian certainly has those as well, though his conflicts with other people are all in the past at this point as he is alone on the hore of the lake.

I will talk first about his internal conflicts and then his external conflicts.

Internal--Brian has had some success at surviving on the shore of the lake. He has learned how to get some foraged foods, how to ration them so he does not make himsef ill from eating too much, how to start a fire, and how to build a rudimentary shelter.  He was even suicidal at the beginning of his survival experience.  He has grown stronger and he reflects on the "old" Brian at this point, well over a month and a half since he was stranded alone. He hates his old self.  He has grown a lot in his time there.  He reflects upon how he has become a part of the forest, just like the bears and other creatures there.

Brian also has internal conflicts from his old life that were unresolved when he landed in the woods.  His parents were getting divorced and Brian had a Secret--he had seen his mother with a strange man before the divorce.  These come up in hs mind from time to time, but the more pressing issues of survival force Brian to focus on the present moment.

Extrenal--

Brian is always in constant conflict with the forest and the forces of nature.  He feels prode in his growth and accomplishments, yet each chapter seems to hand him new conflicts.  In Chapter 13, he wins a victory over nature when he uses his intelligence and skill to catch his first fish.  Seeing that he canuse the entrails of the fish as bait is a major piece of learning as well.  It ensures the future availability of food, and Brian has learned that in the forest food is life.  It is everything.

Brian also makes the mistake of forgetting that a skunk fights back with a scent that temporarially blinds him. Every mistake is both a defeat and a small victory for Brian, because they force him to acquire a greater knowledge about how to deal with the wilderness, and lead him to prepare for the future.