mgr inż. Magdalena Chmara
- Asystent w Katedra Analizy Nieliniowej i Statystyki
In this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.
Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space
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 and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.
wyświetlono 348 razy