Solving Becker's Problem on Periodic Solutions of Parabolic Evolution Equations

We present existence and multiplicity theorems for periodic mild solutions to parabolic evolution equations. Their peculiarity is a link with the spectrum of the generator of the semigroup rather than with the spectrum of the linearized periodic BVP for the evolution equation. They provide a positive solution to the open problem risen by Becker [3], they extend some results of Castro and Lazer [5] from scalar to systems of parabolic equations, and they are new even for finite-dimensional ODEs

On Compactness in Function Spaces

There are shown some implications from pseudocompactness to compactness or sequential compactness. The latter, sequential compactness, is obtained via metrizatio

Chow-Lasota theorem for BVPs of evolution equations

We extend the main result of CHOW-LASOTA [1] to evolution equations and show some applications of the outcome