Orbital stability of periodic standing waves for the logarithmic Klein-Gordon equation

The main goal of this paper is to present orbital stability results of periodic standing waves for the one-dimensional logarithmic Klein-Gordon equation. To do so, we first use compactness arguments and a non-standard analysis to obtain the existence and uniqueness of weak solutions for the associated Cauchy problem in the energy space. Second, we prove the orbital stability of standing waves using a stablity analysis of conservative systems.