Existance after death is possible through memories.
On bodily death, a person most definately continues to exist in a non-physical form. When someone lives their life, they effect other people though interactions and relationships. When that person dies, everyone they have effected still hold on to the memories they have with him or her. These memories could be things that the person taught their friends, family and coworkers. Everything they have learned from that person over time will stay alive with them for the rest of their lives, and eventually be passed on to a younger generation. If a deceased person's knowledge passes on other people, they are in a sense existing through memories.
