There are two problems in the story Peter Pan.  Peter Pan, the title character, does not want to grow up.  He lives in Neverland, but he has a curiosity and a longing for aspects of the real world.  Wendy comes to Neverland, but she must decide whether to stay or return home.

Peter Pan finds growing up to be a deplorable thing.  When he was a baby and overheard his parents discussing his future as a man, he ran away.  Peter Pan wants a carefree life of everlasting youth.  If any of the Lost Boys "seem to be growing up, which is against the rules, Peter thins them out" (Peter Pan, Chapter V).  As adult Wendy explains to her daughter, Jane, "it is only the gay and innocent and heartless who can fly."  Peter Pan does not want to lose these qualities.  He swears off what he sees as the burdens of adulthood.  He has the freedom to be forever young in Neverland.  Despite his desire for youth, he peeks through the window of the Darling nursery at night to observe them and hear the stories.  He has a secret longing for the motherly figure he had for only a day.  Peter Pan finds a compromise to solve his problem.  He asks Wendy to come to Neverland to be a mother figure.

Wendy does go to Neverland with her brothers.  For a time, Wendy stays there and plays the role of mother.  She develops a sense of responsibility to Peter Pan and the Lost Boys.  After a while, she begins to long for her own mother at home.  She reasons that she and her brothers should return home.  Peter shares that his own mother forgot about him after awhile.  Wendy knows that her mother loves her and is probably worried.  She has to decide whether to stay in Neverland or return home.

I am assuming that you are asking for the problems (conflict) in Peter Pan.  

The most obvious example of conflict in the story is that between Peter Pan and Captain Hook; the two characters hate one another and their "crews" follow the examples set by the two.  Another problem is Peter's desire to overcome his human nature and stop aging, which is possible in Neverland but means that he misses out on a basic understanding of "normal" life.  Peter is faced with an emotional attachment to Wendy, in addition, but is challenged by her unwillingness to simply abandon the real world in order to exist in the magical world of Neverland.  Basically, Peter cannot have it all.