Revista de la
Unión Matemática Argentina
Periodic solutions of Euler–Lagrange equations in an anisotropic Orlicz–Sobolev space setting
Fernando D. Mazzone and Sonia Acinas
Volume 60, no. 2 (2019), pp. 323–341

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We consider the problem of finding periodic solutions of certain Euler–Lagrange equations which include, among others, equations involving the $p$-Laplace operator and, more generally, the $(p,q)$-Laplace operator. We employ the direct method of the calculus of variations in the framework of anisotropic Orlicz–Sobolev spaces. These spaces appear to be useful in formulating a unified theory of existence of solutions for such a problem.