**4/18/2005**

**Paschalis Karageorgis**

Northwestern University

**Existence of solutions to the nonlinear wave equation with an inverse-square potential**

Focusing on the nonlinear wave equation with an inverse-square potential, we address the existence of solutions under assumptions which are optimal in some sense. In particular, the well-known theorem of Fritz John for a zero potential is shown to hold for potentials which are not necessarily small or positive.