To existence of completely continuous differential realization second order bilinear system

For a continuous nonlinear infinite-dimensional behavioristic system (dynamical system of J. Willems), a functional-geometric study of the necessary and sufficient conditions for the existence of six non-stationary coefficients-operators of the model of bilinear differential realization of this system in the class of second-order differential equations in a separable Hilbert space is carried out. The case is investigated when the simulated operators are burdened with a condition that ensures the complete continuity of the integral form of the equations of realization in the entropy setting.