Geodesic
Note on the uniqueness of a global positive solution to the second Painlevé equation
Electronic journal of differential equations, Tome 2001 (2001)
Zbl   EuDML
The purpose of this note is to study the uniqueness of solutions to $ u'' -u^3 + (t-c)u = 0$, for $ t \in (0,+\infty)$ with Neumann condition at 0. Assuming a certain conditon at infinity, Helfer and Weissler [6] have found a unique solution. We show that, without any assumptions at infinity, this problem has exactly one global positive solution. Moreover, the solution behaves like $\sqrt{t}$ as $t$ approaches infinity.
Classification : 34B15, 35B05, 82D55
Keywords: second Painlevé equation, Neumann condition, global existence 
Guedda,  Mohammed. Note on the uniqueness of a global positive solution to the second Painlevé equation. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a13/
@article{EJDE_2001__2001__a13,
     author = {Guedda,  Mohammed},
     title = {Note on the uniqueness of a global positive solution to the second {Painlev\'e} equation},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0983.34082},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a13/}
}
TY  - JOUR
AU  - Guedda,  Mohammed
TI  - Note on the uniqueness of a global positive solution to the second Painlevé equation
JO  - Electronic journal of differential equations
PY  - 2001
VL  - 2001
UR  - http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a13/
LA  - en
ID  - EJDE_2001__2001__a13
ER  - 
%0 Journal Article
%A Guedda,  Mohammed
%T Note on the uniqueness of a global positive solution to the second Painlevé equation
%J Electronic journal of differential equations
%D 2001
%V 2001
%U http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a13/
%G en
%F EJDE_2001__2001__a13