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International Journal of Mathematics and Mathematical Sciences - Volume 23 2000, Issue 5, Pages 297-311

Institute of Mathematics, Łódź University, ul. Stefana Banacha 22, Łódź 90-238, Poland

Received 12 December 1994; Revised 30 March 1995

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a Bolza problem governed by a linear time-varyingDarboux-Goursat system and a nonlinear cost functional,without the assumption of the convexity of an integrand withrespect to the state variable. We prove a theorem on the existenceof an optimal process in the classes of absolutely continuoustrajectories of two variables and measurable controls with valuesin a fixed compact and convex set.





Author: Dariusz Idczak and Stanislaw Walczak

Source: https://www.hindawi.com/



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