Homoclinic and heteroclinic solutions for a class of second-order non-autonomous ordinary differential equations: Multiplicity results for stepwise potentials

We prove some multiplicity results for a class of one-dimensional nonlinear Schrödinger-type equations of the form x′′ + 2kx - 2g(t)x3 = 0, where k gt; 0 and the weight g(t) is a positive stepwise function. Instead of the cubic term, more general nonlinearities can be considered as well. © 2013 Ellero and Zanolin.