Abstract
In this paper, we study the generalized quasilinear Schrödinger equations with multiple competing potentials and critical growth, which have appeared from plasma physics as well as high-power ultrashort laser in matter where , , is a even function, , for all , as for some constants and for all . Under suitable assumptions on the potentials , and , we obtain the existence and concentration of positive solutions and prove that the semiclassical solutions with maximum points concentrating at the special set or characterized by , and . Furthermore, for any sequence or , converges in to a ground state solution v of
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