We study the harmonic solutions of periodically perturbed differential equations subjected to a possibly time-dependent constraint. We obtain a degree theoretic condition ensuring a “global branching” result for the nontrivial periodic solutions. The argument stems from a combination of techniques from the theory of Topological Degree and Differential-Algebraic Equations. As an application, the set of harmonic solutions of periodically perturbed implicit differential equations is investigated.
PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PERIODIC CONSTRAINTS / Marco Spadini. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - STAMPA. - 48:(2025), pp. 10588.5007-10588.5015. [10.1002/mma.10588]
PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PERIODIC CONSTRAINTS
Marco Spadini
2025
Abstract
We study the harmonic solutions of periodically perturbed differential equations subjected to a possibly time-dependent constraint. We obtain a degree theoretic condition ensuring a “global branching” result for the nontrivial periodic solutions. The argument stems from a combination of techniques from the theory of Topological Degree and Differential-Algebraic Equations. As an application, the set of harmonic solutions of periodically perturbed implicit differential equations is investigated.
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