Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Multiple homoclinic orbits for autonomous, singular potentials

Ugo Bessia1

a1 Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, Italy

Abstract

We consider the problem

S0308210500028651_eqnU1

where uRn, n ≧ 2, and VC2(Rne, 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.

(Received August 06 1991)

(Revised May 11 1993)