TY - JOUR
AU - Coti Zelati, Vittorio
AU - Rabinowitz, Paul H.
PY - 2001/03/01
Y2 - 2023/02/01
TI - Heteroclinic solutions between stationary points at different energy levels
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 17
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2001.001
SP - 1 - 21
AB - Consider the system of equations$$ -\ddot{q} = a(t)V'(q).$$ The main goal of this paper is to present a simple minimization methodto find heteroclinic connections between isolated critical points of$V$, say $0$ and $\xi$, which are local maxima but do not necessarilyhave the same value of $V$. In particular we prove that there existheteroclinic solutions from $0$ to $\xi$ and from $\xi$ to $0$ for aclass of positive slowly oscillating periodic functions $a$ provided$\delta = |V(0) - V(\xi)|$ is sufficiently small (and anothertechnical condition is satisfied). Note that when $V(0)
eq V(\xi)$,$a$ cannot be constant be conservation of energy. Existence of``multi-bump'' solutions is also proved.
ER -