@Article{Long2011,
author = "Long, Wei and Yang, Jianfu",
title = "Existence and asymptotic behavior of solutions for Hénon type equations",
journal = "Opuscula Math.",
year = "2011",
volume = "31",
number = "3",
pages = "411--424",
doi = "http://dx.doi.org/10.7494/OpMath.2011.31.3.411",
url = "http://dx.doi.org/10.7494/OpMath.2011.31.3.411",
abstract = "This paper is concerned with ground state solutions for the Hénon type equation \(-\Delta u(x)=|y|^{\alpha} u^{p-1}(x)\) in \(\Omega\), where \(\Omega=B^k(0,1)\times B^{n-k}(0,1)\subset \mathbb{R}^n\) and \(x=(y,z) \in \mathbb{R}^k \times \mathbb{R}^{n-k}\). We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions for the problem. We also investigate asymptotic behavior of the ground state solution when \(p\) tends to the critical exponent \(2^*=\frac {2n}{n-2}\) if \(n\geq 3\).",
keywords = "Hénon equation, cylindrical symmetry, non-cylindrical symmetry, asymptotic behavior",
issn = "1232-9274"
}