### On a result of Leizarowitz and Mizel

Alexander J. Zaslavski

#### 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.

#### Article information

Source
Adv. Differential Equations Volume 12, Number 5 (2007), 515-540.

Dates
First available in Project Euclid: 29 April 2013

Mathematical Reviews number (MathSciNet)
MR2321564

Zentralblatt MATH identifier
1148.49002

Subjects
Primary: 49N60: Regularity of solutions