In the present paper we are concerned with the existence of T-periodic solutions for the differential equation x'(t) = f( t, x(t)), where f is a continuous time dependent T-periodic tangent vector field defined on an n-dimensional differentiable manifold M possibly with boundary. We prove that if the Euler characteristic of the average vector field associated to f is defined and nonzero and if suitable a priori bounds on all the possible orbits of the parametrized equation x'(t)= \lambda f(t, x(t)), with \lambda in (0, 1], lie in a compact set and do not hit the boundary of M, then the given equation admits a T-periodic solution.
A continuation principle for forced oscillations on differential manifolds / M. Furi; M.P. Pera. - In: PACIFIC JOURNAL OF MATHEMATICS. - ISSN 0030-8730. - STAMPA. - 121:(1986), pp. 321-338.
A continuation principle for forced oscillations on differential manifolds
FURI, MASSIMO;PERA, MARIA PATRIZIA
1986
Abstract
In the present paper we are concerned with the existence of T-periodic solutions for the differential equation x'(t) = f( t, x(t)), where f is a continuous time dependent T-periodic tangent vector field defined on an n-dimensional differentiable manifold M possibly with boundary. We prove that if the Euler characteristic of the average vector field associated to f is defined and nonzero and if suitable a priori bounds on all the possible orbits of the parametrized equation x'(t)= \lambda f(t, x(t)), with \lambda in (0, 1], lie in a compact set and do not hit the boundary of M, then the given equation admits a T-periodic solution.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.