Continuation theorems for periodic systems and applications to problems with nonlinear time-dependent differential operators

2025/12/25 by Pierluigi Benevieri, Benevieri, Pierluigi, Guglielmo Feltrin +1
Mathematics · Physics and Astronomy · #34B15 #34C25 #47H11 #47J05 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.2512.21554

openalex publication_date 2025/12/25 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28

Abstract

In this paper we propose some continuation theorems for the periodic problem \begincases x_i' = g_i(t,x_i+1), amp;i=1,…,n-1,
x_n' = h(t,x₁,…,x_n),
x_i(0)=x_i(T), amp;i=1,…,n, \endcases providing a unified framework that improves and extends earlier contributions by Jean Mawhin and collaborators to second-order differential problems governed by nonlinear time-dependent differential operators of the form \begincases (ϕ(t,x'))'=f(t,x,x'),
x(0)=x(T), x'(0)=x'(T). \endcases The proof is based on the topological degree theory.

Citations

• An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators

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