Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations

In this paper, we study the following non-autonomous Choquard-Pekar equation: {-Delta u + V(x)u = (W * F(u)) f(u), x is an element of R-N (N >= 2), u is an element of H-1 (R-N), where the potential V (x) is 1-periodic and 0 lies in a gap of the spectrum of the Schrodinger operator -Delta + V. Under some general assumptions on the potential W and the nonlinearity f , we show the existence of ground state solutions. We also construct infinitely many geometrically distinct solutions by using the variational method and deformation arguments. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper studies the non-autonomous Choquard-Pekar equation, under some general assumptions on the potential W and the nonlinearity f, ground state solutions are proved to exist. Infinitely many geometrically distinct solutions are also constructed using the variational method and deformation arguments.