Differential inclusions with constraints in Banach spaces
Here, the author investigates the topological properties of the solution set to a constrained differential inclusion of the form \[ \dot{u}(t)\in F(t,u(t))\text{ a.e. on } I=[0,1],\;f(u(t))\leq 0,\;u(0)=u_0 \] with \(F:I\times U\to 2^{E}\) and \(U\) an open subset of a Banach space \(E\). By assuming that the multivalued term is upper semicontinuous, satisfies a compactness condition (formulated by Kuratowski's measure of noncompactness) and a tangency condition (expressed with the help of Clarke's tangent cone), he proves that the solution set is \(R_\delta\) in \(C(I,E)\). Moreover, he applies this result to investigate the structure of the viable solution set. This way, he generalizes several earlier obtained results.
scientific article; zbMATH DE number 1869657