• Nicholas D. Alikakos
  • Giorgio Fusco
  • Panayotis Smyrnelis
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 91)


We begin by giving a concise proof of the existence of a heteroclinic connection (Theorem 2.1). The experienced reader then can move on to Sect. 2.6. In Sect. 2.4 we develop an alternative approach via constrained minimization. Most readers will find this easier and also good preparation for the polar form and the cut-off lemma in Chap.  4. In Sect. 2.6 we consider the connection problem for an unbalanced double-well potential, and handle it via the constrained method. Finally in Sect. 2.7 we investigate the failure of the existence of a connection when three or more global minima are present.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Nicholas D. Alikakos
    • 1
  • Giorgio Fusco
    • 2
  • Panayotis Smyrnelis
    • 3
  1. 1.Department of MathematicsNational and Kapodistrian UniversityAthensGreece
  2. 2.Department of MathematicsUniversity of L’AquilaCoppitoItaly
  3. 3.Center for Mathematical ModelingUniversity of ChileSantiagoChile

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