Open Access
1998 Existence and uniform boundedness of optimal solutions of variational problems
Alexander J. Zaslavski
Abstr. Appl. Anal. 3(3-4): 265-292 (1998). DOI: 10.1155/S1085337598000566


Given an x0Rn we study the infinite horizon problem of minimizing the expression 0Tf(t,x(t),x(t))dt as T grows to infinity where x:[0,)Rn satisfies the initial condition x(0)=x0. We analyse the existence and the properties of approximate solutions for every prescribed initial value x0. We also establish that for every bounded set ERn the C([0,T]) norms of approximate solutions x:[0,T]Rn for the minimization problem on an interval [0,T] with x(0),x(T)E are bounded by some constant which does not depend on T.


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Alexander J. Zaslavski. "Existence and uniform boundedness of optimal solutions of variational problems." Abstr. Appl. Anal. 3 (3-4) 265 - 292, 1998.


Published: 1998
First available in Project Euclid: 8 April 2003

zbMATH: 0963.49002
MathSciNet: MR1749412
Digital Object Identifier: 10.1155/S1085337598000566

Primary: 49J99 , 58F99

Keywords: Good function , infinite horizon , overtaking optimal function

Rights: Copyright © 1998 Hindawi

Vol.3 • No. 3-4 • 1998
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