Existence and uniform boundedness of optimal solutions of variational problems. (1998)

• Record Type: Journal Article
• Authors: Zaslavski, Alexander J.
• Is Part Of: Abstract and applied analysis. Volume 3:Number 3/4(1998)
• Page Start: 265
• Page End: 292
• Publication Date: 1998
• Subjects: Infinite horizon -- overtaking optimal function -- good function; Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337598000566
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Given anx 0 ∈ R n we study the infinite horizon problem of minimizing the expression∫ 0 T f ( t, x ( t ), x ′ ( t ) ) d t asT grows to infinity wherex : [ 0, ∞ ) → R n satisfies the initial conditionx ( 0 ) = x 0 . We analyse the existence and the properties of approximate solutions for every prescribed initial valuex 0 . We also establish that for every bounded setE ⊂ R n theC ( [ 0, T ] ) norms of approximate solutionsx : [ 0, T ] → R n for the minimization problem on an interval[ 0, T ] withx ( 0 ), x ( T ) ∈ E are bounded by some constant which does not depend onT .