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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.

Heteroclinic solutions to an asymptotically autonomous second-order equation.

Spradlin, Gregory S. (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Heteroclinics for a class of fourth order conservative differential equations

Habets, P., Sanchez, L., Tarallo, M., Terracini, S. (2002)

Equadiff 10

Higher-order Melnikov functions for single-DOF mechanical oscillators: theoretical treatment and applications.

Lenci, Stefano, Rega, Giuseppe (2004)

Mathematical Problems in Engineering

Homoclinic and period-doubling bifurcations for damped systems

Ugo Bessi (1995)

Annales de l'I.H.P. Analyse non linéaire

Homoclinic and periodic solutions of scalar differential delay equations

Hans-Otto Walther (1989)

Banach Center Publications

Homoclinic orbits for a class of infinite dimensional hamiltonian systems

Philippe Clément, Patricio Felmer, Enzo Mitidieri (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3

Joanna Janczewska, Jakub Maksymiuk (2012)

Open Mathematics

We consider a conservative second order Hamiltonian system $\ddot{q} + \nabla V (q) = 0$ in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.

Homoclinic orbits for a class of symmetric Hamiltonian systems.

Korman, Philip, Lazer, Alan C. (1994)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Homoclinic orbits for an almost periodically forced singular Newtonian system in ℝ³

Robert Krawczyk (2015)

Annales Polonici Mathematici

This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in ℝ³ which are subjected to almost periodic forcing in time variable.

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Existence problems for $ω$ -closed orbits.

Fast and heteroclinic solutions for a second order ODE.

First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems.

From transverse heteroclinic cycles to transverse homoclinic orbits

Generalized linking theorem and nonlinear equations in unbounded domains

Global homoclinic bifurcation for damped systems.

Heteroclinic connections for a class of non-autonomous systems.

Heteroclinic orbits in plane dynamical systems