LAUSR

We are concerned with the following quasilinear Schrödinger equations (1) where , are parameters, V and f are nonnegative continuous functions, is a positive bounded function. By using variational methods, we study the existence of positive ground state solutions to problem (1) when V, q and f satisfy some suitable conditions. Furthermore, the concentrating behavior of ground state solutions to problem (1) is proved. We mainly extend the results in Severo, Gloss and da Silva [On a class of quasilinear Schrödinger equations with superlinear or asymptotically linear terms. J Differ Equ. 2017;263:3550–3580], which considered quasilinear Schrödinger equations with positive potential function, to quasilinear Schrödinger equations with steep potential well.