Publications Repository - Gdańsk University of Technology

We will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove the existence of a homoclinic solution, avoiding the singularity, via minimization of an action integral defined in an appropriate Orlicz-Sobolev space. We find a candidate for a solution as weak limit of a minimizing sequence and show directly that it is a critical point of the action functional. Our results extend those by Tanaka in [28].

Authors

• prof. dr hab. Marek Izydorek link open in new tab ,
• prof. dr hab. Joanna Janczewska link open in new tab ,
• dr Nils Waterstraat