It’s not entirely true to say that Christopher is solving his problem by running away; quite the opposite. At some point, he’s going to have to return home, and when he does it’s more than likely that he’ll be treated as abominably by the bullies at school as he was before he ran away. If anything, the likelihood is that Christopher will be subject to even more ridicule, especially since he wrote down his innermost feelings in a letter, thus making him vulnerable to yet more abuse.
Yet Christopher doesn’t simply run away. In his diary entries, he constructs an alternate reality that, whether knowingly or not, forces the people of Steepleton to confront the part they played in creating a society where such appalling treatment could be meted out to a young adult. The fantasy world that Christopher has created in his diary could be construed as his way of dealing with the horrors of daily life.
Ordinary life was so bad for Christopher that the only way he could deal with it was by creating a world of his own, the only world where he could truly feel safe and secure. This may not, strictly speaking, constitute dealing with his problems, but under the circumstances, it’s the only way he knows how.