Periodic solutions with prescribed minimal period for second-order Hamiltonian systems with non-symmetric potentials

In this paper, inspired by the works of Szulkin and Weth in 2009 and Pankov in 2007, we develop a new approach to study the Rabinowitz's conjecture on the existence of periodic solutions with prescribed minimal period for second -order Hamiltonian system without any symmetric assumptions. Specifically, we first obtain the ground state solution of Nehari-Pankov type for the Hamiltonian system by using Linking theorem and approximation. Then we show that the ground state solution is the desired periodic solution. As a result, we prove that the Rabinowitz's conjecture holds true in the case when the potential satisfies an additional assumption.