On Li-Lin's open problem

Abstract

In this paper, we give a first negative answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3): 943-968, 2012). Meanwhile we also give a second positive answer to the Li-Lin's open problem. The first positive answer was given by G. Cerami, X. Zhong and W. Zou (Calc. Var. Partial Differential Equations, 54(2): 1793-1829, 2015).