68 research outputs found
Periodic perturbations of constrained motion problems on a class of implicitly defined manifolds
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.Comment: 15 pages, 2 figures, to appear in Communications in Contemporary
Mathematics. arXiv admin note: substantial text overlap with arXiv:1102.156
On a class of differential-algebraic equations with infinite delay
We study the set of -periodic solutions of a class of -periodically
perturbed Differential-Algebraic Equations, allowing the perturbation to
contain a distributed and possibly infinite delay. Under suitable assumptions,
the perturbed equations are equivalent to Retarded Functional (Ordinary)
Differential Equations on a manifold. Our study is based on known results about
the latter class of equations.Comment: 13 pages. Revision: Incorporate changes suggested by readers.
Corrected a few typos across the paper, definition of BU added, revised the
(previously incorrect) definition of solution of RFDAE, made slight changes
in the Introduction. Replacement of Dec. 6, 2012: introduced further changes
suggested by referee, bundled addendum/erratum containing a corrected version
of Lemma 5.5 and Corollary 5.
About the notion of non--resonance and applications to topological multiplicity results for ODEs on differentiable manifolds
By using topological methods, mainly the degree of a tangent vector field, we
establish multiplicity results for -periodic solutions of parametrized
-periodic perturbations of autonomous ODEs on a differentiable manifold .
In order to provide insights into the key notion of -resonance, we consider
the elementary situations and . So doing, we
provide more comprehensive analysis of those cases and find improved
conditions.Comment: 10 figure
Periodic solutions of semi-explicit differential-algebraic equations with time-dependent constraints
In this paper we investigate the properties of the set of T-periodic
solutions of semi-explicit parametrized Differential-Algebraic Equations with
non-autonomous constraints of a particular type. We provide simple, degree
theoretic conditions for the existence of branches of T-periodic solutions of
the considered equations. Our approach is based on topological arguments about
differential equations on implicitly defined manifolds, combined with
elementary facts of matrix analysis
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