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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair

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Volume 18, Issue 2


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

Giovanni Vidossich
Published Online: 2018-02-08 | DOI: https://doi.org/10.1515/ans-2017-6047


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.

Keywords: Compact Semigroups; Spectral Properties; Topological Degree; Periodic Solutions,Parabolic Equations; ODEs

MSC 2010: 47D60; 35K55; 34B15

Dedicated to my friends Lily and Ronnie Becker, for their 50th wedding anniversary.


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About the article

Received: 2017-08-08

Revised: 2018-01-09

Accepted: 2018-01-10

Published Online: 2018-02-08

Published in Print: 2018-04-01

Citation Information: Advanced Nonlinear Studies, Volume 18, Issue 2, Pages 195–215, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2017-6047.

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