Periodic solutions of differential systems with curvature-like principal part and unbounded nonlinearity

Marco Degiovanni; Valentina Folloni

doi:10.3934/dcdss.2025058

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2026, Volume 20: 110-142. Doi: 10.3934/dcdss.2025058

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Periodic solutions of differential systems with curvature-like principal part and unbounded nonlinearity

Marco Degiovanni^{1, 2, ,} and
Valentina Folloni^1,

1.
Università Cattolica del Sacro Cuore, Italy
2.
Istituto Lombardo Accademia di Scienze e Lettere, Italy

^*Corresponding author: Marco Degiovanni
^*Corresponding author: Marco Degiovanni

Received: March 2025

Early access: April 25, 2025

Published online: April 25, 2025

The first author is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Abstract

We consider a Lagrangian system with a curvature-like principal part. Under suitable assumptions, we prove the existence of a nonconstant periodic solution. For this purpose, nonsmooth variational methods are applied.

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Mathematics Subject Classification: Primary: 37J46; Secondary: 58E05, 70H12.

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References

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