Arcwise connectedness of solution sets to of an infinite horizon nonlinear integrodifferential inclusion (Q2755011)

The author studies the integro-differential system \(x'(t)\in F(t,x(t),V(x)(t)), x(0)=\xi\) where the operator \(V:C([0,\infty),\mathbb{R}^n)\to C([0,\infty),\mathbb{R}^n)\) is defined by \(V(x)(t)=\int_{0}^{t}k(t,s,x(s))ds\). The main result the states arcwise connectedness of the solution set to that system. This extends a result by \textit{V. Staicu} [Arcwise connectedness of solution sets to differential inclusions, Technical Report CM/I 41, Aveiro University (1998)] concerning the common differential system \(x'(t)\in F(t,x(t)), x(0)=\xi\).