Abstract
In this work, we study the existence of positive ground states and concentration phenomena for the following class of quasilinear Schrödinger equations: where is a parameter, is a continuously differentiable function, and are positive and bounded continuous potentials and the nonlinearity can exhibit critical exponential growth. In order to prove our concentration result, we exploit variational arguments that take into account an interaction between the potentials V and Q, in combination with the Trudinger–Moser inequality and Moser iteration method.
Acknowledgements
We would like to thank the referees for careful reading of the paper with many useful comments and important suggestions, which substantially helped improving the quality of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).