We look for T-periodic solutions on a convex Riemannian manifold M of the differential equation Dsẋ(s)+ ▽Vz(x(s),s) = 0 where Dsẋ(s) is the covariant derivative of ẋ(s), V is a C2 real function on M × R, T-periodic in s. The manifold is allowed to be noncompact and to have boundary, so the action integral associated to the equation does not satisty the Palais-Smale compactness condition. We overcome this problem under a assumption on the sectional curvature of M which allows to control the Morse index of the critical points of f at "infinity". If M has a "rich" topology it is proved tha there exist infinitely many periodic solutions.

Periodic orbits on Riemannian manifolds with convex boundary / Bartolo, Rossella. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 3:3(1997), pp. 439-450. [10.3934/dcds.1997.3.439]

Periodic orbits on Riemannian manifolds with convex boundary

Bartolo, Rossella
1997-01-01

Abstract

We look for T-periodic solutions on a convex Riemannian manifold M of the differential equation Dsẋ(s)+ ▽Vz(x(s),s) = 0 where Dsẋ(s) is the covariant derivative of ẋ(s), V is a C2 real function on M × R, T-periodic in s. The manifold is allowed to be noncompact and to have boundary, so the action integral associated to the equation does not satisty the Palais-Smale compactness condition. We overcome this problem under a assumption on the sectional curvature of M which allows to control the Morse index of the critical points of f at "infinity". If M has a "rich" topology it is proved tha there exist infinitely many periodic solutions.
1997
Periodic orbits on Riemannian manifolds with convex boundary / Bartolo, Rossella. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 3:3(1997), pp. 439-450. [10.3934/dcds.1997.3.439]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/2471
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