Ground state solutions for Choquard equations with Bessel potential

Abstract

Firstly, we study the existence, regularity and decay of positive solutions for the elliptic system where , g satisfies Berestycki-Lions type conditions. In Sobolev space, the system can be transformed into the Choquard equations with Bessel potential where is the fundamental solution of the linear operator on . Moreover, by assuming that g is nondecreasing, we obtain the radial symmetry and monotonic property of positive solutions by moving plane method, and the existence of ground state solutions by non-Nehari manifold method.