Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry
Electronic journal of differential equations, Tome 2003 (2003)
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.
@article{EJDE_2003__2003__a176,
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},
year = {2003},
volume = {2003},
zbl = {1109.35321},
language = {en},
url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a176/}
}
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 UR - http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a176/ LA - en ID - EJDE_2003__2003__a176 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 %U http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a176/ %G en %F EJDE_2003__2003__a176
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__a176/