This internship concerns universal properties of near threshold bound states or quasi bound sates of non relativistic particles, that can be deduced by means of singularities in the wave function corresponding thus to a zero range potential model of the interactions. In this modeling, valid when one considers length scales larger than the range of the interactions, the problem can be mapped onto a 2D effective Schrödinger equation with a pure inverse square law potential. At the unitary limit (i.e. for an arbitrarily large value of the two-body scattering length), in some systems (as for instance for three identical bosons), this potential is attractive leading to the Efimov effect with an infinite number of bound states and a geometric spectrum. This phenomenon has been studied in details since its observation in ultracold atoms in 2006. The other class of systems where this potential is repulsive received less attention although applying to various situations where the bound states correspond to isolated (or accidental) resonances. The internship is in the continuity of recent works on this subject by considering specific three-body problems and possibly the link with finite range models where the resonance comes from an attractive character of the interaction at small distance.