TY  - JOUR
ID  - Long2011
LB  - Long2011
AU  - Long, Wei
AU  - Yang, Jianfu
TI  - Existence and asymptotic behavior of solutions for Hénon type equations
ST  - Existence and asymptotic behavior of solutions for Hénon type equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2011
VL  - 31
IS  - 3
SP  - 411
EP  - 424
DO  - http://dx.doi.org/10.7494/OpMath.2011.31.3.411
UR  - http://dx.doi.org/10.7494/OpMath.2011.31.3.411
AB  - 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 \(n\geq 3\).
KW  - Hénon equation
KW  - cylindrical symmetry
KW  - non-cylindrical symmetry
KW  - asymptotic behavior
SN  - 1232-9274
ER  -