TY - JOUR ID - 1002 TI - Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Shi, H. AU - Chen, H. AD - School of Mathematics and Statistics‎, ‎Central South University‎, ‎Changsha‎, ‎410083 Hunan‎, ‎P‎. ‎R‎. ‎China. Y1 - 2017 PY - 2017 VL - 43 IS - 1 SP - 147 EP - 161 KW - Kirchhoff-type equations KW - Critical growth KW - variational methods DO - N2 - 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. UR - http://bims.iranjournals.ir/article_1002.html L1 - http://bims.iranjournals.ir/article_1002_618460655d8d3715c47ad9fa384f957c.pdf ER -