Differential and Integral Equations

Nonexistence and uniqueness for biharmonic problems with supercritical growth and domain geometry

Saïma Khenissy

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


We prove nonexistence and uniqueness results of positive solutions for biharmonic supercritical equations $\Delta ^2 u = f(u)$ under Navier boundary conditions on a smooth bounded domain $\Omega \subset \mathbb{R}^N$. The results stand for suitable supercritical nonlinearities $f$ with some geometrical conditions on $ \Omega.$ We define the $h$-starlikeness of $\Omega$ and a classifying number $M(\Omega)$. This allows us to define a generalized critical exponent for these domains which play the role of the classical exponent $\frac{N+4}{N-4}$. Our approach is based on Rellich-Pohozaev type estimates. In particular, we construct some $h $-starlike domains which are topologically nontrivial where our results can apply.

Article information

Differential Integral Equations, Volume 24, Number 11/12 (2011), 1093-1106.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J40: Boundary value problems for higher-order elliptic equations 35J30: Higher-order elliptic equations [See also 31A30, 31B30] 35J60: Nonlinear elliptic equations


Khenissy, Saïma. Nonexistence and uniqueness for biharmonic problems with supercritical growth and domain geometry. Differential Integral Equations 24 (2011), no. 11/12, 1093--1106. https://projecteuclid.org/euclid.die/1356012878

Export citation