Valence and oscillation of functions in the unit disk.
We establish several variational inclusions for solutions of a nonconvex Sturm-Liouville type differential inclusion on a separable Banach space.
We establish new conjugacy criteria for half-linear second order differential equations. These criteria are based on the relationship between conjugacy of the investigated equation and nonpositivity of the associated energy functional.
A variational formula for positive functionals of a Poisson random measure and brownian motion is proved. The formula is based on the relative entropy representation for exponential integrals, and can be used to prove large deviation type estimates. A general large deviation result is proved, and illustrated with an example.