Differential and Integral Equations

Linear perturbations for the critical Hénon problem

Francesca Gladiali and Massimo Grossi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper, we study the problem \begin{equation} \left\{\begin{array}{ll} -\Delta u=|x|^\alpha u^{p_\alpha}+{\epsilon}|x|^{{\beta}}u & \hbox{ in }\Omega\\ u>0 & \hbox{ in }\Omega\\ u=0 & \hbox{ on }{\partial}\Omega, \end{array}\right. \end{equation} where $p_\alpha=\frac{N+2+2\alpha}{N-2}$, $\Omega$ is a smooth bounded domain of ${\mathbb R}^N$ with $0\in\Omega$ and $N\ge4$. We show that, for $\alpha\ge0$ and $0\le{\beta}\le N-4$, there exists one solution concentrating at $x=0$ as ${\epsilon}\rightarrow0$. Moreover, we prove that, if $\Omega$ is a ball, there exist no radial solution if $\alpha={\beta}>N-4$.

Article information

Differential Integral Equations, Volume 28, Number 7/8 (2015), 733-752.

First available in Project Euclid: 11 May 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J15: Second-order elliptic equations


Gladiali, Francesca; Grossi, Massimo. Linear perturbations for the critical Hénon problem. Differential Integral Equations 28 (2015), no. 7/8, 733--752. https://projecteuclid.org/euclid.die/1431347861

Export citation