Multiple homoclinic solutions for a one-dimensional Schr\uf6dinger equation

In this paper we study the problem of the existence of homoclinic solutions to a Schrodinger equation of the form x''-V(t)x+x(3)=0, where V is a stepwise potential. The technique of proof is based on a topological method, relying on the properties of the transformation of continuous planar paths (the S.A.P. method), together with the application of the classical Conley-Wazewski method