2008/01/01 by Nicholas D. Alikakos, N. D. Alikakos, Giorgio Fusco +1 · 4 citations
Mathematics · Physics and Astronomy · #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · doi:10.1512/iumj.2008.57.3181
crossref issued 2008/01/01 · crossref published 2008/01/01 · crossref published-print 2008/01/01 · openalex publication_date 2008/01/01 · crossref created 2008/09/02 · crossref deposited 2011/07/26 · openalex created_date 2025/10/10 · crossref indexed 2026/07/28 · openalex updated_date 2026/07/28
The problem considered is the existence of heteroclinic connections for Hamiltonian systems of N 2nd order differential equations with potential possessing possibly more than two global minima. First restricting to potentials with exactly two global minima we give an existence theorem under very weak nondegeneracy hypotheses on the potential. Our approach is variational: we prove existence by showing that the Action functional has a minimizer on the set of maps connecting the two minima. Next, allowing more than two minima but restricting to systems of two 2nd order equations, we analyze the phenomenon of nonexistence. In particular, by extending a result from [3], we conclude that generally nonexistence is robust under small analytic perturbations of the potential.