Properties of the solution set of nonlinear evolution inclusions
The paper deals with nonlinear nonautonomous evolution inclusions of the form \[ \dot x(t)+ A(t,x(t)) \in F(t,x(t)), \] a.e. on \(T\), \(x(0) =x_0\) defined on a Gelfand triple of spaces \((X,H,X^*)\). In Section 3 the authors provide conditions for the solution set to be an \(R_\delta\)-set, or path-connected in \(C(T,H)\). An invariance result is given in Section 4, together with a result on the existence of periodic solutions. In the last section applications of these results are given for some parabolic partial differential equations with multivalued terms.
nonlinear nonautonomous evolution inclusions
parabolic partial differential equations
scientific article; zbMATH DE number 1047002
scientific article