Existence of positive solutions for a class of p&qp&q elliptic problems with critical growth on RNRN

This paper is concerned with the existence of positive solutions to the class of p&qp&q elliptic problems with critical growth type−div(a(|∇u|p)|∇u|p−2∇u)+b(|u|p)|u|p−2u=λf(u)+|u|γ⁎−2u,u(z)>0,∀x∈RN, where λ   is a positive parameter, a:R→Ra:R→R is a function of C1C1 class and b,f:R→Rb,f:R→R are continuous functions.