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The purpose of this paper is to discuss the variational problems and the optimal control problems characterized by a system of nonlinear Volterra integral equations. The necessary conditions are obtained, for cases both with or without restricted phase coordinates, in the integral form of the maximum principle.

In this paper, we study necessary conditions for an optimal control problem both with and without restricted phase coordinates. The systems are specified by differential-difference equations with their allowed right-hand sides being a quasiconvex family. The multiplier rule developed by Neustadt is used, and maximum principles in integral form as well as in pointwise form are obtained.

In this paper, we use the e-technique developed by Balakrishnan to derive the maximum principle for systems with delay elements both in state space and control function.

1. After 14 days on a diet containing 5 or 25% casein male rats received a fracture of the left femur. Four hours before they were killed the injured and control rats were injected with [1-14C]leucine; the incorporation of radioactivity into an isolated fraction of skeletal muscle ribosomes was studied 6, 12, 24, 48, 72, 96 and 228 h after injury.2. The incorporation of [14C]leucine into the ribosome fraction in right thigh muscles dropped to 40% of control values 72 h after fracture in well-nourished rats and after 96 h with diets containing 5 or 25%, casein.3. The specific activity of the trichloroacetic acid-soluble fraction of muscle from injured rats was equal to or higher than that of the controls during the first 72 h but lower at 96 h.4. These results suggest that a reduced incorporation of amino acids by ribosomes from the right thigh muscle occurred on day 3 after fracture in the group receiving 25% casein but not in the group receiving 5% casein.5. Muscle RNA and DNA concentrations were not affected by the injury.6. The relationship between these findings and the loss of muscle N after injury is discussed.