On a fractional Kirchhoff system with logarithmic nonlinearities

Abstract

In this paper, two results regarding the existence and multiplicity of ground state solutions for a fractional Kirchhoff-type system involving logarithmic nonlinearities are obtained via variational methods. The proposed problem is motivated by several mathematical models that arise, for example, in quantum mechanics, nuclear physics, quantum optics, transport and diffusion phenomena, effective quantum gravity, open quantum systems, the theory of superfluidity, and Bose–Einstein condensation. The first result provides the existence of a ground state solution for the proposed problem. Under a different set of hypotheses with respect to the first result, a second one is obtained, which provides the existence of at least two non-trivial ground state solutions.