Heteroclinic solutions between stationary points at different energy levels
Keywords
Heteroclinic solutions, variational methods, Lagrangian systemsAbstract
Consider the system of equations $$ -\ddot{q} = a(t)V'(q). $$ The main goal of this paper is to present a simple minimization method to find heteroclinic connections between isolated critical points of $V$, say $0$ and $\xi$, which are local maxima but do not necessarily have the same value of $V$. In particular we prove that there exist heteroclinic solutions from $0$ to $\xi$ and from $\xi$ to $0$ for a class of positive slowly oscillating periodic functions $a$ provided $\delta = |V(0) - V(\xi)|$ is sufficiently small (and another technical condition is satisfied). Note that when $V(0) \neq V(\xi)$, $a$ cannot be constant be conservation of energy. Existence of ``multi-bump'' solutions is also proved.Downloads
Published
2001-03-01
How to Cite
1.
COTI ZELATI, Vittorio and RABINOWITZ, Paul H. Heteroclinic solutions between stationary points at different energy levels. Topological Methods in Nonlinear Analysis. Online. 1 March 2001. Vol. 17, no. 1, pp. 1 - 21. [Accessed 14 February 2025].
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