Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation

D. Bonheure; L. Sanchez; M. Tarallo; S. Terracini
August 2003
Calculus of Variations & Partial Differential Equations;Aug2003, Vol. 17 Issue 4, p341
Academic Journal
Assuming that f is a potential having three minima at the same level of energy, we study for the conservative equation $$ u�{iv}-g(u)u��>-\frac{1}{2}g'(u)u'�2+f'(u)=0,$$ the existence of a heteroclinic connection between the extremal equilibria. Our method consists in minimizing the functional $$\int_{-\infty}�{+\infty}\left[\frac{1}{2}[(u��>{}�2)+g(u)u'{}�2]+f(u)\right] dx$$ whose Euler-Lagrange equation is given by (1), in a suitable space of functions.


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