On solutions of hyperbolic differential inclusions with nonconvex right-hand side

The existence of a generalized solution with continuous derivativesu_x,u_y is proved for the differential inclusionu_xyF(x, y, u) with a nonconvex right-hand side satisfying the Lipschitz conditioninx, y, andu.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 531–534, April, 1995.