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On a result of Leizarowitz and Mizel. (English) Zbl 1148.49002

Summary: A. Leizarowitz and V. J. Mizel [Arch. Ration. Mech. Anal. 106, No. 2, 161–193 (1989; Zbl 0672.73010)] 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.

MSC:

49J27 Existence theories for problems in abstract spaces
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids

Citations:

Zbl 0672.73010
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