On the existence of heteroclinic connections

  • Giorgio FuscoEmail author
  • Giovanni F. Gronchi
  • Matteo Novaga


Assume that \(W:\mathbb {R}^m\rightarrow \mathbb {R}\) is a nonnegative potential that vanishes only on a finite set A with at least two elements. By direct minimization of the action functional on a suitable set of maps we give a new elementary proof of the existence of a heteroclinic orbit that connects any given \(a_-\in A\) to some \(a_{+}\in A{\setminus }\{a_{-}\}\).


Heteroclinic orbit Action functional Jacobi functional Minimization 

Mathematics Subject Classification

37J50 37J45 



G.F.G. has been partially supported by the University of Pisa via Grant PRA-2017 “Sistemi dinamici in analisi, geometria, logica, e meccanica celeste”. M.N. was partially supported by GNAMPA and by the University of Pisa via Grant PRA-2017 “Problemi di ottimizzazione ed evoluzione in ambito variazionale”.


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Copyright information

© Instituto de Matemática e Estatística da Universidade de São Paulo 2017

Authors and Affiliations

  1. 1.Università dell’AquilaL’AquilaItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di PisaPisaItaly

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