Geodesic
Existence of positive solutions to a superlinear elliptic problem
Electronic journal of differential equations, Tome 2001 (2001)
We study the existence of positive solutions to the semilinear elliptic problem

$ - \epsilon^2 \Delta u + V(z) u = f(u) $

in $\mathbb{R}^N (N\geq 2)$, where the function $f$ has superlinear growth at infinity without any restriction from above on its growth.
Classification : 35J20, 35J10, 35A15
Keywords: superlinear, mountain pass, Schrödinger equation, elliptic equation 
@article{EJDE_2001__2001__a172,
     author = {Alves,  C.O. and Miyagaki,  O.H.},
     title = {Existence of positive solutions to a superlinear elliptic problem},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0967.35042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a172/}
}
TY  - JOUR
AU  - Alves,  C.O.
AU  - Miyagaki,  O.H.
TI  - Existence of positive solutions to a superlinear elliptic problem
JO  - Electronic journal of differential equations
PY  - 2001
VL  - 2001
UR  - http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a172/
LA  - en
ID  - EJDE_2001__2001__a172
ER  - 
%0 Journal Article
%A Alves,  C.O.
%A Miyagaki,  O.H.
%T Existence of positive solutions to a superlinear elliptic problem
%J Electronic journal of differential equations
%D 2001
%V 2001
%U http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a172/
%G en
%F EJDE_2001__2001__a172
Alves,  C.O.; Miyagaki,  O.H. Existence of positive solutions to a superlinear elliptic problem. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a172/