Repozytorium publikacji - Politechnika Gdańska

Abstract. This paper is concerned with the following Euler-Lagrange system d/dtLv(t,u(t), ̇u(t)) =Lx(t,u(t), ̇u(t)) for a.e.t∈[−T,T], u(−T) =u(T), Lv(−T,u(−T), ̇u(−T)) =Lv(T,u(T), ̇u(T)), where Lagrangian is given by L=F(t,x,v) +V(t,x) +〈f(t),x〉, growth conditions aredetermined by an anisotropic G-function and some geometric conditions at infinity.We consider two cases: with and without forcing termf. Using a general version ofthe mountain pass theorem and Ekeland’s variational principle we prove the existenceof at least two nontrivial periodic solutions in an anisotropic Orlicz-Sobolev space.

Autorzy

• dr inż. Magdalena Chmara link otwiera się w nowej karcie