@article {
author = {Shi, H. and Chen, H.},
title = {Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {1},
pages = {147-161},
year = {2017},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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.},
keywords = {Kirchhoff-type equations,Critical growth,variational methods},
url = {http://bims.iranjournals.ir/article_1002.html},
eprint = {http://bims.iranjournals.ir/article_1002_618460655d8d3715c47ad9fa384f957c.pdf}
}