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Prescribed energy connecting orbits for gradient systems

2019
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Discrete and Continuous Dynamical Systems. Series A
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We are concerned with conservative systemsq = ∇V (q), q ∈ R N for a general class of potentials V ∈ C 1 (R N ). Assuming that a given sublevel set {V ≤ c} splits in the disjoint union of two closed subsets V c − and V c + , for some c ∈ R, we establish the existence of bounded solutions qc to the above system with energy equal to −c whose trajectories connect V c − and V c + . The solutions are obtained through an energy constrained variational method, whenever mild coerciveness properties are

doi:10.3934/dcds.2019200
fatcat:2hxrwvnsxnb4nhxjcc75bvdkqm