Some existence results on periodic solutions of Euler-Lagrange equations in an Orlicz-Sobolev space

S. ACINAS; L.BURI; G. GIUBERGIA; F. MAZZONE; E. SCHWINDT

JOURNAL OF NONLINEAR ANALYSIS

PERGAMON-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2015 vol. 125 p. 681 - 698

0362-546X

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^1L^Phi associated to an N-function Phi. We show that, in some sense, it is necessary for the coercitivity that the complementary function of Phi satisfy the Delta_2-condition. We conclude by discussing conditions for the existence of minima of I.