Geodesic
Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle
Electronic journal of differential equations, Tome 2000 (2000)
In this paper we study the existence of concentrated solutions of the nonlinear field equation $###$, the potential $V$ is positive and radial, and $W$ is an appropriate singular function satisfying a suitable symmetric property. Provided that $h$ is sufficiently small, we are able to find solutions with a certain spherical symmetry which exhibit a concentration behaviour near a circle centered at zero as $h\to 0^{+}$. Such solutions are obtained as critical points for the associated energy functional; the proofs of the results are variational and the arguments rely on topological tools. Furthermore a penalization-type method is developed for the identification of the desired solutions.
Classification : 35J20, 35J60
Keywords: nonlinear Schrödinger equations, topological charge, existence, concentration 
@article{EJDE_2000__2000__a193,
     author = {D'Aprile,  Teresa},
     title = {Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: {Concentration} around a circle},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0954.35057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a193/}
}
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JO  - Electronic journal of differential equations
PY  - 2000
VL  - 2000
UR  - http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a193/
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%A D'Aprile,  Teresa
%T Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle
%J Electronic journal of differential equations
%D 2000
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%F EJDE_2000__2000__a193
D'Aprile,  Teresa. Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle. Electronic journal of differential equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a193/