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