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Multiple homoclinic orbits for autonomous, singular potentials

Published online by Cambridge University Press:  14 November 2011

Ugo Bessi
Ugo Bessi
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, Italy
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Abstract

We consider the problem

where u ∊ Rn, n ≧ 2, and V ∊ C2(Rn∖e, R) is a potential having an absolute maximum at 0 and such that V(x) → − ∞ as x → e. We prove that, under some conditions on V, this problem has at least n − 1 geometrically distinct solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 4 , 1994 , pp. 785 - 802
Copyright
Copyright © Royal Society of Edinburgh 1994

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