Key points are not available for this paper at this time.
In this paper, we are concerned with the ground states of the following planar Kirchhoff-type problem: \ - (1+bₑℂ| u|²\, dx) u+ u=|u|^p-2u, x². \ where b, \, >0 are constants, p>2. Based on variational methods, regularity theory and Schwarz symmetrization, the equivalence of ground state solutions for the above problem with the minimizers for some minimization problems is obtained. In particular, a new scale technique, together with Lagrange multipliers, is delicately employed to overcome some intrinsic difficulties.
Lei et al. (Mon,) studied this question.