Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation

Details Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation

2004-12-06

arxiv.org/abs/math/0412105v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

In this paper, we consider a biharmonic equation under the Navier boundary condition and with a nearly critical exponent $(P_\epsilon): \Delta^2u=u^{9-\epsilon}, u>0$ in $\Omega$ and $u=\Delta u=0$ on $\partial\Omega$, where $\Omega$ is a smooth bounded domain in $\R^5$ and $\epsilon >0$. We study the asymptotic behavior of solutions of $(P_\epsilon)$ which are minimizing for the Sobolev qutient as $\epsilon$ goes to zero. We show that such solutions concentrate around a point $x_0\in\Omega$ as $\epsilon\to 0$, moreover $x_0$ is a critical point of the Robin's function. Conversely, we show that for any nondegenerate critical point $x_0$ of the Robin's function, there exist solutions concentrating around $x_0$ as $\epsilon$ goes to zero.

Affiliated with

Also associated with

No associations

Rating

Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-41085