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Periodic solutions for nonlinear nonmonotone evolution inclusions

  • * Corresponding author: Leszek Gasiński

    * Corresponding author: Leszek Gasiński 
The first author was supported by the National Science Center of Poland under Project no. 2015/19/B/ST1/01169
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  • 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.

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


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