Concentrating ground state solutions for quasilinear Schrodinger equations with steep potential well

摘要

We are concerned with the following quasilinear Schrodinger equations { -Delta u + lambda V(x)u +kappa/2 Delta(u(2))u = q(x)f (u), x is an element of R-N, uH(1)(R-N), (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 Schrodinger equations with superlinear or asymptotically linear terms. J Differ Equ. 2017;263:3550-3580, which considered quasilinear Schrodinger equations with positive potential function, to quasilinear Schrodinger equations with steep potential well.