Assuming that f is a potential having three minima at the same level of energy, we study for the conservative equation uiv - g(u)u″ - 1/2g′(u)u′2 + f′(u) = 0, (1) the existence of a heteroclinic connection between the extremal equilibria. Our method consists in minimizing the functional ∫-∞ +∞[1/2[(u″2) + g(u)u′2] + f(u)] dx whose Euler-Lagrange equation is given by (1), in a suitable space of functions.
Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation / D. Bonheure, L. Sanchez, M.E. Tarallo, S. Terracini. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 17:4(2003), pp. 341-356.
Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation
M.E. TaralloPenultimo
;
2003
Abstract
Assuming that f is a potential having three minima at the same level of energy, we study for the conservative equation uiv - g(u)u″ - 1/2g′(u)u′2 + f′(u) = 0, (1) the existence of a heteroclinic connection between the extremal equilibria. Our method consists in minimizing the functional ∫-∞ +∞[1/2[(u″2) + g(u)u′2] + f(u)] dx whose Euler-Lagrange equation is given by (1), in a suitable space of functions.
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