Heteroclinic orbits in plane dynamical systems

Luisa Malaguti and Cristina Marcelli

Address. L. Malaguti, Department of Pure and Applied Mathematics ``G. Vitali", University of Modena and Reggio Emilia, via Campi 213/B, 41100 Modena, ITALY

C. Marcelli, Department of Mathematics ``V.Volterra", University of Ancona, via Brecce Bianche - 60131 Ancona, ITALY

E-mail: malaguti.luisa@unimo.it, marcelli@dipmat.unian.it

Abstract. We consider general second order boundary value problems on the whole line of the type $u''=h(t,u,u')$, $u(-\infty)=0, u(+\infty)=1$, for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the $(u,u')$ plane dynamical system.

AMSclassification. Primary: 34C37; Secondary: 34B16, 34B40, 37C29.

Keywords. Nonlinear boundary value problems, heteroclinic solutions, lower and upper solutions, singular boundary value problems.