In the Short story " The liar" by Tobias Wolff who is the solipsist? the mother or the son?
If I might evade your question, I think they both are to some extent. I am defining solipsist not as the story does, but rather as dictionaries do -- someone who thinks they are the only one that truly exists.
I don't think either of them truly believes this, but I think that they both sometimes act as if they do. They both act at times as if the world is just supposed to be set up the way they want it.
James does this by lying all the time. I think he lies so as to define his own reality -- to make the world be the way he wants it.
His mother does it by trying to control everything. She wants to control how James acts at the funeral. She wants to control how her husband will die. She tries to force James to roughhouse and do things that he doesn't want to.
So they both seem to be trying to set their worlds up the way they want them to be. But don't we all?