We consider an open connected set Ω and a smooth potential U which is positive in Ω and vanishes on âΩ. We study the existence of orbits of the mechanical system u¨=Ux(u), that connect different components of âΩ and lie on the zero level of the energy. We allow that âΩ contains a finite number of critical points of U. The case of symmetric potential is also considered.
On the existence of connecting orbits for critical values of the energy
Gronchi, Giovanni F.;Novaga, Matteo
2017-01-01
Abstract
We consider an open connected set Ω and a smooth potential U which is positive in Ω and vanishes on âΩ. We study the existence of orbits of the mechanical system u¨=Ux(u), that connect different components of âΩ and lie on the zero level of the energy. We allow that âΩ contains a finite number of critical points of U. The case of symmetric potential is also considered.File in questo prodotto:
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