Abstract
In this paper we study resonances and eigenvalues for the nonlinear constant mean curvature equation linearized around the bubbles found by Brezis-Coron. This nonlinear equation is also called a H-system equation. For degree one bubbles we only find resonances. For higher degree we prove eigenvalues occur. Our goal is to eventually obtain dispersive estimates for the wave equation associated to the linear and non-linear problem, a study of which was initiated by Chanillo-Yung.