Mountain pass type periodic solutions for Euler-Lagrange equations in anisotropic Orlicz-Sobolev space
- Resource Type
- Working Paper
- Authors
- Chmara, Magdalena; Maksymiuk, Jakub
- Source
- Subject
- Mathematics - Analysis of PDEs
Mathematics - Classical Analysis and ODEs
- Language
Using the Mountain Pass Theorem, we establish the existence of periodic solution for Euler-Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part $K-W$ and a forcing term. We consider two situations: $G$ satisfying $\Delta_2\cap\nabla_2$ in infinity and globally. We give conditions on the growth of the potential near zero for both situations.