Geodesic
Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Positive entire solutions of the singular biharmonic equation $\Delta^2 u + u^{-q}=0$ in $\mathbb{R}^n$ with $q geater than 1$ and $n\geq 3$ are considered. We prove that there are infinitely many radial entire solutions with different growth rates close to quadratic. If $u(0)$ is kept fixed we show that a unique minimal entire solution exists, which separates the entire solutions from those with compact support. For the special case $n=3$ and $q=7$ the function $U(r) = \sqrt{1/\sqrt{15}+r^2}$ is the minimal entire solution if $u(0)=15^{-1/4}$ is kept fixed.
Classification : 35J60
Keywords: singular biharmonic equation, conformal invariance 
@article{EJDE_2003__2003__a76,
     author = {McKenna, P. J. and Reichel, Wolfgang},
     title = {Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a76/}
}
TY  - JOUR
AU  - McKenna, P. J.
AU  - Reichel, Wolfgang
TI  - Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry
JO  - Electronic Journal of Differential Equations
PY  - 2003
VL  - 2003
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a76/
LA  - en
ID  - EJDE_2003__2003__a76
ER  - 
%0 Journal Article
%A McKenna, P. J.
%A Reichel, Wolfgang
%T Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry
%J Electronic Journal of Differential Equations
%D 2003
%V 2003
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a76/
%G en
%F EJDE_2003__2003__a76
McKenna, P. J.; Reichel, Wolfgang. Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a76/