Eugenio Montefusco

Learn More
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.
In this paper we investigate a Dirichlet problem in a strip and, using the sliding method, we prove monotonicity for positive and bounded solutions. We obtain uniqueness of the solution and show that this solution is a function of only one variable. From these qualitative properties we deduce existence of a classical solution for this problem.
  • 1