Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation

Abstract

The authors study the Lagrangian stability for the sublinear Duffing equations ẍ + e(t)∣x∣ ^α−1 x = p(t) with 0 < α < 1, where e and p are real analytic quasi-periodic functions with frequency ω. It is proved that if the mean value of e is positive and the frequency ω satisfies Diophantine condition, then every solution of the equation is bounded.

Keywords

Hamiltonian system / Sublinear Duffing equation / Boundedness / Quasi-periodic solution / Invariant curve

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