Periodic solutions for nonlinear nonmonotone evolution inclusions

Leszek Gasiński; Nikolaos S. Papageorgiou

doi:10.3934/dcdsb.2018015

Article Contents

2018, Volume 23, Issue 1: 219-238. Doi: 10.3934/dcdsb.2018015

This issue Previous Article Multiplicity results for discrete anisotropic equations Next Article Qualitative properties of solutions of higher order difference equations with deviating arguments

Periodic solutions for nonlinear nonmonotone evolution inclusions

Leszek Gasiński^1, , and
Nikolaos S. Papageorgiou^2,

1.
Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Łojasiewicza 6, 30-348 Kraków, Poland
2.
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece

* Corresponding author: Leszek Gasiński
* Corresponding author: Leszek Gasiński

Received: July 31, 2016

Revised: May 31, 2017

Published: November 2017

The first author was supported by the National Science Center of Poland under Project no. 2015/19/B/ST1/01169

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Abstract

We study periodic problems for nonlinear evolution inclusions defined in the framework of an evolution triple $(X,H,X^*)$ of spaces. The operator $A(t,x)$ representing the spatial differential operator is not in general monotone. The reaction (source) term $F(t,x)$ is defined on $[0,b]× X$ with values in $2^{X^*}\setminus\{\emptyset\}$. Using elliptic regularization, we approximate the problem, solve the approximation problem and pass to the limit. We also present some applications to periodic parabolic inclusions.

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Mathematics Subject Classification: Primary: 34G20; Secondary: 35K85.

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