A Sturm-Liouville theorem for some odd multivalued maps

Abstract:

Let $T:H \to {2^H}$ be the subdifferential of a real l. s. c. convex function on an infinite dimensional, separable, real Hilbert space $H$. Assuming that $T$ is odd (i.e. $T( - u) = - Tu,\;\forall u\;\epsilon H)$), $0\epsilon T(0),\;{(I + T)^{ - 1}}$ is compact and $T(0)$ satisfies a geometrical condition, we prove that $T$ has an infinite sequence $\{ {\lambda _n}\}$ of eigenvalues such that $0 \leqslant {\lambda _{n \overrightarrow n }} + \infty$.