Please give an example of person vs self-conflict within Into the Wild.
I am not quite sure I understand your question or that the question actually makes sense, but it is clear that you are asking about conflict in this novel and how it progresses. One great example to look at is the conflict that exists between his parents before he embarks on his quest for transcendental enlightenment. A very revealing piece of information is given to us in Chapter Three, when he writes a letter to Carrie bemoaning the way that his parents offered to buy him a new car and also fund him through law school:
I'm going to have to be real careful not to accept any gifts from then in the future because they will think they have bought my respect.
Clearly this letter indicates the conflict between Chris and his parents, and the mutual lack of understanding between them. It was, of course, shortly after this that Chris cut all contact with his parents and left to hit the road.
Another, far more interesting element of conflict lies in the discrepancy between the imagination of Chris and how he is inspired by the works of Jack London and the actual hum-drum reality of London's life. The author comments:
He was so enthralled by these tales, however, that he seemed to forget that were works of fiction, constructions of the imagination that had more to do with London's romantic sensibilities than with the actualities of life in the subarctic wilderness. McCandless conveniently overlooked the fact that London himself had spent just a single winter in the North and that he'd died by his own hand on his California estate at the age of forty, a fatuous drunk, obese and pathetic, maintaining a sedentary existence that bore scant resemblance to the ideals he espoused in print.
This points at a deep inner-conflict that Chris McCandless chose to ignore. In seeking to live out the lives of the characters in London's fiction, he forgets that their lives were just that--fiction.
Alexander Supertramp's entire journey is a conflict between himself. He struggles with leaving his family, and he struggles in his travels with his attitudes towards the people he meets. When he gets to Alaska, he struggles with whether he should go on and keep moving or to try to go home. Many of his struggles come after he's sort of trapped there in Alaska. He has a lot of thoughts about his life, but he's also thinking that he should go home and he begins to feel bad about being out there with no one knowing where he is. These are all examples of Self vs. Self conflict in the story. Enotes has a very good analysis of the themes that may help you further with this concept.