In this article, we consider the p-Kirchhoff type problem
(1+Ξ»β«RNββ£βuβ£p+Ξ»bβ«RNββ£uβ£p)(βΞpβu+bβ£uβ£pβ2u)=f(u),xβRN,
where Ξ»>0, the nonlinearity f can reach critical growth.
Without the Ambrosetti-Robinowitz condition or the monotonicity condition
on f, we prove the existence of positive solutions for the p-Kirchhoff
type problem. In addition, we also study the asymptotic behavior of the
solutions with respect to the parameter Ξ»β0