Alessandro Calamai, Marco Spadini
Abstract:
We study the structure of the set of harmonic solutions to \(T\)-periodically
perturbed coupled differential equations on differentiable manifolds, where the
perturbation is allowed to be of Caratheodory-type regularity.
Employing degree-theoretic methods, we prove the existence of a noncompact connected
set of nontrivial \(T\)-periodic solutions that, in a sense, emanates from the set of
zeros of the unperturbed vector field. The latter is assumed to be degenerate:
Meaning that, contrary to the usual assumptions on the leading vector field,
it is not required to be either trivial nor to have a compact set of zeros.
In fact, known results in the nondegenerate case can be recovered from our ones.
We also provide some illustrating examples of Lienard- and \(\phi\)-Laplacian-type
perturbed equations.
Submitted January 12, 2024. Published July 9, 2024.
Math Subject Classifications: 34C25, 34C40, 34C23, 47H11.
Key Words: Coupled differential equations on manifolds; topological degree; branches of periodic solutions; Carath\'eodory vector field.
DOI: 10.58997/ejde.2024.39
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Alessandro Calamai Dipartimento di Ingegneria Civile, Edile e Architettura Università Politecnica delle Marche Via Brecce Bianche, I-60131 Ancona, Italy email: a.calamai@univpm.it |
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Marco Spadini Dipartimento di Matematica e Informatica "Ulisse Dini'' Università degli Studi di Firenze Via S. Marta 3, I-50139 Florence, Italy email: marco.spadini@unifi.it |
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