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In this paper orbital stability of solutions of weakly coupled nonlinear Schrödinger equations is studied. It is proved that ground state solutions-scalar or vector ones-are orbitally stable , while bound states with Morse index strictly greater than one are not stable. Moreover, an instability result for large exponent in the nonlinearity is presented.

We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.

The semiclassical limit of a weakly coupled nonlinear focusing Schrödinger system in presence of a nonconstant potential is studied. The initial data is of the form (u 1 , u 2) with u i = r i x−˜x ε e i ε x·˜ξ , where (r 1 , r 2) is a real ground state solution, belonging to a suitable class, of an associated autonomous elliptic system. For ε sufficiently… (More)

We study the spectral structure of the complex linearized operator for a class of nonlinear Schrödinger systems, obtaining as byproduct some interesting properties of non-degenerate ground state of the associated elliptic system, such as being isolated and orbitally stable.

In this paper we prove existence and multiplicity results of unbounded critical points for a general class of weakly lower semicontinuous functionals. We will apply a nonsmooth critical point theory developed in [10, 12, 13] and applied in [8, 9, 20] to treat the case of continuous functionals.

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