Heteroclinic connections for a class of non-autonomous systems.
We consider general second order boundary value problems on the whole line of the type , , for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the plane dynamical system.
Sufficient conditions for the existence of solutions to boundary value problems with a Caratheodory right hand side for ordinary differential systems are established by means of continuous approximations.