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.
18
2
195
215
Vidossich, Giovanni
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/86286
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