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The heteroclinic connection problem for general double-well potentials. (English) Zbl 1383.37052

Summary: By variational methods, we provide a simple proof of existence of a heteroclinic orbit to the Hamiltonian system \(u''=\nabla W(u)\) that connects the two global minima of a double-well potential \(W\). Moreover, we consider several inhomogeneous extensions.

MSC:

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
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