We study forced oscillations on differentiable manifolds which are globally defined as the zero set of appropriate smooth maps in some Euclidean spaces. Given a T-periodic perturbative forcing field, we consider the two different scenarios of a nontrivial unperturbed force field and of perturbation of the zero field. We provide simple, degree-theoretic conditions for the existence of branches of T-periodic solutions. We apply our construction to a class of second-order differential-algebraic equations.
Periodic perturbations of constrained motion problems on a class of implicitly defined manifolds / Alessandro Calamai;Marco Spadini. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 17:(2015), pp. 1-19. [10.1142/S0219199714500278]
Periodic perturbations of constrained motion problems on a class of implicitly defined manifolds
SPADINI, MARCO
2015
Abstract
We study forced oscillations on differentiable manifolds which are globally defined as the zero set of appropriate smooth maps in some Euclidean spaces. Given a T-periodic perturbative forcing field, we consider the two different scenarios of a nontrivial unperturbed force field and of perturbation of the zero field. We provide simple, degree-theoretic conditions for the existence of branches of T-periodic solutions. We apply our construction to a class of second-order differential-algebraic equations.File | Dimensione | Formato | |
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