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.
Solving Becker's Problem on Periodic Solutions of Parabolic Evolution Equations / Vidossich, Giovanni. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 18:2(2018), pp. 195-215. [10.1515/ans-2017-6047]
Solving Becker's Problem on Periodic Solutions of Parabolic Evolution Equations
Vidossich, Giovanni
2018-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
