Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 8.7

Center Manifolds and Bifurcation Theory

Mathematics — Calculus · mathieu-equation-periodic-solutions

Problem

Show that Mathieu's equation u′′+(ω2+εcos⁡t)u=0u'' + (\omega^2 + \varepsilon \cos t)u = 0 has no nonzero 2π2\pi-periodic solutions for ω≠1,2,…\omega \neq 1, 2, \ldots, when ε\varepsilon is small enough.

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