Periodic solutions for nonlinear nonmonotone evolution inclusions
Leszek Gasiński, Νικόλαος Παπαγεωργίου · Discrete and Continuous Dynamical Systems - B · 2017
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.