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 W1LΦ associated to an N-function Φ. We show that, in some sense, it is necessary for the coercivity that the complementary function of Φ satisfy the Δ2-condition. We conclude by discussing conditions for the existence of minima of I.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.