Stationary Kirchhoff Equations Involving Critical Growth and Vanishing Potential

We establish the existence of positive solutions for a class of stationary Kirchhoff-type equations defined in the whole R 3 involving critical growth in the sense of the Sobolev embedding and potentials, which may decay to zero at infinity. We use minimax techniques combined with an appropriate truncated argument and a priori estimate. These results are new even for the local case, which corresponds to nonlinear Schrödinger equations. © EDP Sciences, SMAI 2020.