Initial and boundary value problems for nonconvex valued multivalued functional differential equations (Q1412383)

The authors consider the functional-differential inclusion \[ (\rho(t)y'(t))'\in F(t,y_t)\tag{1} \] on the interval \([0,T]\), together with initial conditions \[ y_0=\phi,\qquad y'(0)=\eta,\tag{2} \] or boundary conditions \[ y_0=\phi,\qquad y(T)=\eta,\tag{3} \] respectively. Here, \(F:[0,T]\times C([-r,0];\mathbb{R}^n)\to {\mathcal P}(\mathbb{R}^n)\) is a multivalued map, \(\phi\in C([-r,0];\mathbb{R}^n)\), \(\rho\in C([0,T];\mathbb{R}_+)\), \(\eta\in \mathbb{R}^n\), and \({\mathcal P}(\mathbb{R}^n)\) is the family of all subsets of \(\mathbb{R}^n\). Existence results for \((1)\), \((2)\), resp. for \((1)\), \((3)\), are established.