Geodesic
Point rupture solutions of a singular elliptic equation
Electronic journal of differential equations, Tome 2013 (2013)
We consider the elliptic equation

$ \Delta u=f(u) $

in a region

$ \lim_{u\to 0^{+}}f(u) =\infty. $

Motivated by the thin film equations, a solution $u$ is said to be a point rupture solution if for some $p\in\Omega, u(p) =0$ and $u(p) >0$ in $\Omega\backslash\{ p\} $. Our main result is a sufficient condition on f for the existence of radial point rupture solutions.
Classification : 49Q20, 35J60, 35Q35
Keywords: thin film, point rupture, radial solution, singular equation 
@article{EJDE_2013__2013__a124,
     author = {Jiang,  Huiqiang and Miloua,  Attou},
     title = {Point rupture solutions of a singular elliptic equation},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1294.35033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a124/}
}
TY  - JOUR
AU  - Jiang,  Huiqiang
AU  - Miloua,  Attou
TI  - Point rupture solutions of a singular elliptic equation
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a124/
LA  - en
ID  - EJDE_2013__2013__a124
ER  - 
%0 Journal Article
%A Jiang,  Huiqiang
%A Miloua,  Attou
%T Point rupture solutions of a singular elliptic equation
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a124/
%G en
%F EJDE_2013__2013__a124
Jiang,  Huiqiang; Miloua,  Attou. Point rupture solutions of a singular elliptic equation. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a124/