On multiplicity and concentration of positive solutions for a class of quasilinear problems with critical exponential growth in RNRN

In this work we study the existence, multiplicity and concentration of positive solutions for the following class of quasilinear problems−ϵNΔNu+V(x)|u|N−2u=f(u)in RN,u(x)>0,∀x∈RN, where ΔNuΔNu is the N  -Laplacian operator, ϵ is a positive parameter, N⩾2N⩾2, V:RN→R is a continuous function and f:R→R is a C1C1 function having critical exponential growth.