International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 5, Pages 297-311
doi:10.1155/S0161171200000880
Abstract
We consider a Bolza problem governed by a linear time-varying
Darboux-Goursat system and a nonlinear cost functional,
without the assumption of the convexity of an integrand with
respect to the state variable. We prove a theorem on the existence
of an optimal process in the classes of absolutely continuous
trajectories of two variables and measurable controls with values
in a fixed compact and convex set.