Semiclassical ground state solutions for a Schrödinger equation in with critical exponential growth

Abstract

Consider a Schrödinger equation urn:x-wiley:0025584X:media:mana201400267:mana201400267-math-0002where and are two continuous real functions on , ε is a positive parameter, the nonlinearity f is assumed to be of critical exponential growth in the sense of the Trudinger‐Moser inequality. By truncating the potentials and , we are able to establish some new existence and concentration results for critical Schrödinger equation in by variational methods. As a particular case, we observe that the concentration appears at the maximum set of the nonlinear potential which complements the results in , .