Nonconvex and nonmonotone perturbations of evolution inclusions of subdifferential type
The note contains an existence theorem for strong solutions of differential inclusions \(\dot x(t)\in -\partial \phi (x(t))-F(t,x(t)),\) in a separable Hilbert space. Here \(\partial \phi\) is the subdifferential of a proper lower semicontinuous convex function \(\phi\) with precompact level sets, and F is a measurable lower semicontinuous multifunction. If \(| F(t,x)|\) is dominated by \(\alpha| \partial \phi (x)|\) with \(\alpha <1\), then a local solution is constructed by means of a fixed point argument. The solution exists globally if an additional one- sided growth assumption holds.
scientific article; zbMATH DE number 4200664
scientific article