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Some existence results on periodic solutions of Euler–Lagrange equations in an Orlicz–Sobolev space setting
Abstract : In this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations. We employ the direct method of the calculus of variations, i.e. we obtain solutions minimizing certain functional I. We give conditions which ensure that I is finitely defined and differentiable on certain subsets of Orlicz-Sobolev spaces W 1 L Φ associated to an N-function Φ. We show that, in some sense, it is necessary for the coercitivity that the complementary function of Φ satisfy the ∆ 2-condition. We conclude by discussing conditions for the existence of minima of I.
Cited literature [36 references]
https://hal.archives-ouvertes.fr/hal-01171091
Contributor : Erica Schwindt Connect in order to contact the contributor
Submitted on : Monday, July 6, 2015 - 11:46:27 AM
Last modification on : Tuesday, October 12, 2021 - 5:20:12 PM
Long-term archiving on: : Tuesday, April 25, 2017 - 10:10:18 PM
Contributor : Erica Schwindt Connect in order to contact the contributor
Submitted on : Monday, July 6, 2015 - 11:46:27 AM
Last modification on : Tuesday, October 12, 2021 - 5:20:12 PM
Long-term archiving on: : Tuesday, April 25, 2017 - 10:10:18 PM
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LagrangianoOrliczEnviado.pdf
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