%0 Journal Article
%T Existence and asymptotic behavior of solutions for H¨Śnon type equations
%A Wei Long
%A Jianfu Yang
%J Opuscula Mathematica
%D 2011
%I AGH University of Science and Technology
%X This paper is concerned with ground state solutions for the H¨Śnon type equation $-\Delta u(x)=|y|^{\alpha} u^{p-1}(x)$ in $\Omega$, where $\Omega=B^k(0,1)\times B^{n-k}(0,1)\subset \r^n$ and $x=(y,z) \in \r^k imes \r^{n-k}.$ 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 $n\geq 3.$
%K H¨Śnon equation
%K cylindrical symmetry
%K non-cylindrical symmetry
%K asymptotic behavior
%U http://www.opuscula.agh.edu.pl/vol31/3/art/opuscula_math_3129.pdf