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In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius $\mu$ in $L_p$ $(p>1)$. It is proved that the set of trajectories generated by all admissible control functions is Lipschitz continuous with respect to $\mu$ for each fixed $p$, and is continuous with respect to $p$ for each fixed $\mu$. An upper...