Multiplicity of positive solutions for a class of problems with exponential critical growth in R2R2

Using variational methods we establish multiplicity of positive solutions for the following class of problems−Δu+(λV(x)+Z(x))u=f(u),u>0in R2, where λ∈(0,∞),fλ∈(0,∞),f is a continuous function with exponential critical growth and V,Z:R2→R are continuous functions verifying some hypotheses.