Differential and Integral Equations

A compactness type result for Paneitz-Branson operators with critical nonlinearity

K. Sandeep

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

Abstract

Given $(M,g),$ a compact Riemannian manifold of dimension $n \ge 8,$ we consider positive solutions $u_{\alpha} $ of ${\Delta}^2_gu - div_g(A_{\alpha} du) + a_{\alpha} u = u^{2^\sharp-1}$, where $ A_{\alpha}$ is a smooth, symmetric (2,0) tensor and $a_{\alpha}$ a smooth function. Assuming that $ A_{\alpha}$ and $a_{\alpha}$ converge in a suitable sense as ${\alpha} \rightarrow \infty$, we obtain conditions under which the weak limit of $u_{\alpha}$ is nontrivial.

Article information

Source
Differential Integral Equations, Volume 18, Number 5 (2005), 495-508.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060182

Mathematical Reviews number (MathSciNet)
MR2136976

Zentralblatt MATH identifier
1212.35092

Subjects
Primary: 58J05: Elliptic equations on manifolds, general theory [See also 35-XX]
Secondary: 35B33: Critical exponents 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations 58J60: Relations with special manifold structures (Riemannian, Finsler, etc.)

Citation

Sandeep, K. A compactness type result for Paneitz-Branson operators with critical nonlinearity. Differential Integral Equations 18 (2005), no. 5, 495--508. https://projecteuclid.org/euclid.die/1356060182


Export citation