Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation

Bonheure, Denis;Sanchez, L.;Tarallo, M;Terracini, S
(2003) Calculus of Variations and Partial Differential Equations — Vol. 17, n° 4, p. 341-356 (2003)

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  • Bonheure, DenisUCLouvain
    Author
  • Sanchez, L.
    Author
  • Tarallo, M
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  • Terracini, S
    Author
Abstract
Assuming that f is a potential having three minima at the same level of energy, we study for the conservative equation u(iv)-g(u)u"-1/2g'(u)'(2)+f'(u)=0 (1) the existence of a heteroclinic connection between the extremal equilibria. Our method consists in minimizing the functional integral(-infinity)(+infinity) [1/2[(u"(2))+(u)u'(2)]+f(u)]dx whose Euler-Lagrange equation is given by (1), in a suitable space of functions.
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Bonheure, D., Sanchez, L., Tarallo, M., & Terracini, S. (2003). Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation. Calculus of Variations and Partial Differential Equations, 17(4), 341-356. https://doi.org/10.1007/s00526-002-0172-y (Original work published 2003)