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2007 On a result of Leizarowitz and Mizel
Alexander J. Zaslavski
Adv. Differential Equations 12(5): 515-540 (2007).

Abstract

Leizarowitz and Mizel (1989) studied a class of one-dimensional infinite horizon variational problems arising in continuum mechanics and established that these problems possess periodic solutions. They considered a one-parameter family of integrands and show the existence of a constant $c$ such that if a parameter is larger than or equal to $c$, then the corresponding variational problem has a solution which is a constant function, while if a parameter is less than $c$, then the corresponding variational problem possesses only non-constant periodic solutions. In this paper we generalize this result for a large class of families of integrands.

Citation

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Alexander J. Zaslavski. "On a result of Leizarowitz and Mizel." Adv. Differential Equations 12 (5) 515 - 540, 2007.

Information

Published: 2007
First available in Project Euclid: 29 April 2013

zbMATH: 1148.49002
MathSciNet: MR2321564

Subjects:
Primary: 49N60
Secondary: 65K10

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 5 • 2007
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