Opuscula Math. 31, no. 3 (2011), 411-424
http://dx.doi.org/10.7494/OpMath.2011.31.3.411

 
Opuscula Mathematica

Existence and asymptotic behavior of solutions for Hénon type equations

Wei Long
Jianfu Yang

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.

Mathematics Subject Classification: 35J50, 35J55, 35J60.

Full text (pdf)

  • Wei Long
  • Jiangxi Normal University, Department of Mathematics, Nanchang, Jiangxi 330022, People’s Republic of China
  • Jianfu Yang
  • Jiangxi Normal University, Department of Mathematics, Nanchang, Jiangxi 330022, People’s Republic of China
  • Received: 2010-08-30.
  • Accepted: 2010-10-29.
Opuscula Mathematica - cover

Cite this article as:
Wei Long, Jianfu Yang, Existence and asymptotic behavior of solutions for Hénon type equations, Opuscula Math. 31, no. 3 (2011), 411-424, http://dx.doi.org/10.7494/OpMath.2011.31.3.411

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.