A note on global classical solutions to a Cauchy problem

S. Ilter, H. Duru, H. N. Öztürk, S. Koca

In this paper, we study the Cauchy problem associated with first-order differential inclusion and present some results on approximation and existence of global classical solution to the problem without convexity and compactness assumptions. For this purpose, we make use successive continuously differentiable approximations for Lipschitzian set-valued maps with nonconvex values. Thus we show that the results about continuously differentiable version of the famous Filippov's theorem still hold in the nonconvex case. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16,  supplement issue 4 (2023), pp. 133-138