Some results on semilinear systems on the unbounded space R.
We study in this paper some systems, using standard tools devoted to the analysis of semilinear elliptic problems on R. These systems do not admit any non trivial radial solutions in the E E = + 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...