Subharmonic Solutions In Reversible Non-Autonomous Differential Equations

2020/08/18 by Izuchukwu Eze, Eze, Izuchukwu, Carlos García-Azpeitia +5 · 3 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2008.08132

openalex publication_date 2020/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the existence of subharmonic solutions in the system u(t)=f(t,u(t)), where u(t)∈ℝ^k and f is an even and p-periodic function in time. Under some additional symmetry conditions on the function f, the problem of finding mp-periodic solutions can be reformulated in a functional space as a Γ×ℤ₂× D_m% -equivariant equation, where the group Γ×ℤ₂ acts on the space ℝ^k and D_m acts on u(t) by time-shifts and reflection. We apply Brouwer equivariant degree to prove the existence of an infinite number of subharmonic solutions for the function f that satisfies additional hypothesis on linear behavior near zero and the Nagumo condition at infinity. We also discuss the bifurcation of subharmonic solutions when the system depends on an extra parameter.

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