Existence of two periodic solutions to general anisotropic Euler-Lagrange equations (Q2233617)

The author considers an Euler-Lagrange system with a Lagrangian of the type \({\mathcal L}=F(t,x,v)+V(t,x)+\langle f(t),x\rangle\) under some periodic-like boundary conditions, i.e., \(u(-T)=u(T)\) and \({\mathcal L}_v(-T,u(-T),\dot u(-T))={\mathcal L}_v(T,u(T),\dot u(T))\). By the use of variational methods, she proves the existence of solutions in an anisotropic Orlicz-Sobolev space.