• elliptic system
• ground states
• Nehari manifold
• Schrodinger equation

The aim of this thesis is to study a generalisation of the Nehari manifold method applied to a class of non linear Schrodinger systems. In particular, we consider stationary solutions so that the problem becomes elliptic. We study how, definining the generalised Nehari manifold appropriately, we are able to prove the existence of a positive solution with "spikes" near strict local minima points of the potential and whose energy is concentrated near these minima, and this energy can be estimated in terms of the ground state energy of particular systems with constant potential.