Existence and uniform boundedness of optimal solutions of variational problems

Alexander J. Zaslavski

Abstract and Applied Analysis, 1998, vol. 3, issue 3-4, 265-292

Abstract: Given an x0 ∈ Rn 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 E ⊂ Rn 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.

Date: 1998
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https://doi.org/10.1155/S1085337598000566

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:3:y:1998:i:3-4:p:265-292

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