%0 Journal Article %T Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Shi, H. %A Chen, H. %D 2017 %\ 02/22/2017 %V 43 %N 1 %P 147-161 %! Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth %K Kirchhoff-type equations %K Critical growth %K variational methods %R %X In this paper‎, ‎we consider the following Kirchhoff-type equations‎: ‎$-‎\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)\Delta u+V(x) u=\lambda$ $f(x,u)+u^{5}‎, ‎\quad \mbox{in }\mathbb{R}^{3},$ ‎$u(x)>0‎, ‎\quad \mbox{in }\mathbb{R}^{3},$ ‎$u\in H^{1}(\mathbb{R}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $\lambda$ is a positive parameter‎. ‎The aim of this paper is to study the existence of positive solutions for Kirchhoff-type equations with a nonlinearity in the critical growth under some suitable assumptions on $V(x)$ and $f(x,u)$‎. ‎Recent results from the literature are improved and extended. %U http://bims.iranjournals.ir/article_1002_618460655d8d3715c47ad9fa384f957c.pdf