- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
29
2013
3
Infinitely many nonradial solutions for the Hénon equation with critical growth
Juncheng
Wei
University of British Columbia, VANCOUVER, CANADA
Shusen
Yan
University of New England, ARMIDALE, AUSTRALIA
Hénon's equation, infinitely many solutions, critical Sobolev exponent, reduction method
We consider the following Hénon equation with critical growth: \[ (*) \begin{cases} - \Delta u = |y|^\alpha \, u^{\frac{N+2}{N-2}},\; u>0, & y\in B_1(0) , \\ u=0, &\text{on } \partial B_1(0), \end{cases} \] where $ \alpha>0$ is a positive constant, $ B_1(0)$ is the unit ball in $\mathbb{R}^N$, and $N\ge 4$. Ni [9] proved the existence of a radial solution and Serra [12] proved the existence of a nonradial solution for $\alpha$ large and $N \geq 4$. In this paper, we show the existence of a nonradial solution for any $\alpha>0$ and $N \geq 4$. Furthermore, we prove that equation (*) has infinitely many nonradial solutions, whose energy can be made arbitrarily large.
Partial differential equations
Operator theory
997
1020
10.4171/RMI/747
http://www.ems-ph.org/doi/10.4171/RMI/747