The present paper is devoted to weighted nonlinear Schrödinger–Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.
Bonheure, D., Di Cosmo, J., & Mercuri, C. (2012). Concentration on circles for nonlinear Schrödinger-Poisson systems with unbounded potentials vanishing at infinity. Communications in Contemporary Mathematics, 14(2), 1250009-1/31. . https://doi.org/10.1142/S0219199712500095