## Advances in Differential Equations

### Critical growth biharmonic elliptic problems under Steklov-type boundary conditions

#### Abstract

We study the fourth-order nonlinear critical problem $\Delta^2 u= u^{2^*-1}$ in a smooth, bounded domain $\Omega \subset \mathbb{R}^n$, $n \ge 5$, subject to the boundary conditions $u=\Delta u-d u_\nu=0$ on $\partial \Omega$. We provide estimates for the range of parameters $d \in \mathbb{R}$ for which this problem admits a positive solution. If the domain is the unit ball, we obtain an almost complete description.

#### Article information

Source
Adv. Differential Equations Volume 12, Number 4 (2007), 381-406.

Dates
First available in Project Euclid: 18 December 2012

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