Advances in Differential Equations

Bifurcation and symmetry breaking for the Henon equation

Anna Lisa Amadori and Francesca Gladiali

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In this paper, we consider the problem $$ \left\{ \begin{array}{ll} -\Delta u=|x|^{\alpha}u^p & \text{ in } B ,\\ u>0 & \hbox{ in } B ,\\ u=0 & \hbox{ on }\partial B , \end{array}\right. $$ where $ B $ is the unit ball of $\mathbb R^N$, $N\ge 3$, $p > 1$ and $0 < \alpha\leq 1$. We prove the existence of (at least) one branch of non-radial solutions that bifurcate from the radial ones and that this branch is unbounded.

Article information

Adv. Differential Equations, Volume 19, Number 7/8 (2014), 755-782.

First available in Project Euclid: 6 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35B40: Asymptotic behavior of solutions 35J61: Semilinear elliptic equations


Amadori, Anna Lisa; Gladiali, Francesca. Bifurcation and symmetry breaking for the Henon equation. Adv. Differential Equations 19 (2014), no. 7/8, 755--782.

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