Nonautonomous Young Differential Equations Revisited

Nonautonomous Young Differential Equations Revisited

In this paper we prove that under mild conditions a nonautonomous Young differential equation possesses a unique solution which depends continuously on initial conditions. The proofs use estimates in p -variation norms, the construction of greedy sequence of times, and Gronwall-type lemma with the h...

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Veröffentlicht in:Journal of dynamics and differential equations 2018, Vol.30 (4), p.1921-1943
Hauptverfasser: Cong, Nguyen Dinh, Duc, Luu Hoang, Hong, Phan Thanh
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Differential equations
Fixed points (mathematics)
Initial conditions
Mathematics
Mathematics and Statistics
Norms
Ordinary Differential Equations
Partial Differential Equations
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Zusammenfassung:In this paper we prove that under mild conditions a nonautonomous Young differential equation possesses a unique solution which depends continuously on initial conditions. The proofs use estimates in p -variation norms, the construction of greedy sequence of times, and Gronwall-type lemma with the help of Shauder theorem of fixed points.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-017-9634-y