Ground state solutions for a (p,q)-Choquard equation with a general nonlinearity

Abstract

In this paper, we study the existence of ground state solutions for the following (p,q)-Choquard equation:−Δpu−Δqu+|u|p−2u+|u|q−2u=(Iα⁎F(u))f(u) in RN, where 2≤p<q<N, Δs is the s-Laplacian operator, with s∈{p,q}, Iα is the Riesz potential of order α∈((N−2q)+,N), F∈C1(R,R) is a general nonlinearity of Berestycki-Lions type and F′=f. Furthermore, we analyze the regularity, symmetry and decay properties of these solutions. In particular, we extend the results in [33] to the (p,q)-Laplacian setting.

Topics & Concepts