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September/October 2009 Heteroclinics for non-autonomous second-order differential equations
A. Gavioli, L. Sanchez
Differential Integral Equations 22(9/10): 999-1018 (September/October 2009).

Abstract

We investigate new conditions for the existence of heteroclinics connecting $\pm 1$ for a non-autonomous equation of the form \begin{equation} \label{hetero} \ddot u=a(t)f(u) \end{equation} where $a(t)$ is a bounded positive function and $f(\pm 1)=0$. Here $f=F'$, where $F$ is a $C^1$ non-negative function such that $F(-1)=F(1)=0$. We are interested mainly in the case where $a(t)$ approaches its positive limit, as $|t|\to\infty$, from above, but we allow also the (``asymptotically asymmetric") case where $|\lim _{t\to-\infty}a(t)-\lim _{t\to+\infty}a(t)|$ is a sufficiently small positive number. Variational methods are used in the proofs.

Citation

Download Citation

A. Gavioli. L. Sanchez. "Heteroclinics for non-autonomous second-order differential equations." Differential Integral Equations 22 (9/10) 999 - 1018, September/October 2009.

Information

Published: September/October 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.34227
MathSciNet: MR2553067

Subjects:
Primary: 34C37

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.22 • No. 9/10 • September/October 2009
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