We study in this paper some systems, using standard tools devoted to the analysis of semilinear elliptic problems on R3. These systems do not admit any non trivial radial solutions in the E1 E2 = + 1 cases. A first type of solution consists in a ground state of R (-1,-1), exhibited by variational arguments, whose structure is a finite energy perturbation of a non trivial constant solution of R (-1,-1). A second type consists in a radial, oscillating, asymptotically null at infinity solution in the E1 E2 = + 1 cases that we exhibit using eigenvalue comparison and ordinary differential equation type arguments.
@article{urn:eudml:doc:44394,
title = {Some results on semilinear systems on the unbounded space R3.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {13},
year = {2000},
pages = {207-229},
zbl = {0972.65090},
mrnumber = {MR1794911},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44394}
}
Mercier, J. M. Some results on semilinear systems on the unbounded space R3.. Revista Matemática de la Universidad Complutense de Madrid, Tome 13 (2000) pp. 207-229. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44394/