1. Solutions of mountain pass type for double well potential systems.
- Author
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Montecchiari, Piero and Rabinowitz, Paul H.
- Subjects
- *
MOUNTAIN pass theorem , *POTENTIAL theory (Mathematics) , *HAMILTONIAN systems , *EXISTENCE theorems , *FUNCTIONALS - Abstract
This paper studies a Hamiltonian system possessing a double well potential for which the existence of multitransition heteroclinic and homoclinic solutions that are local minimizers of an associated functional is known. Under an additional mild non-degeneracy condition on the set of all homoclinic and heteroclinic solutions, the existence of further heteroclinic and homoclinic solutions that are of mountain pass type is established. A key tool for the existence arguments is a variant of the Mountain Pass Theorem that is of independent interest. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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