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The authors discuss the existence of pseudo almost periodic solutions of differential equations with piecewise constant argument by means of introducing new concept, pseudo almost periodic sequence. [ABSTRACT FROM AUTHOR]

The authors study the Lagrangian stability for the sublinear Duffing equations ẍ + e(t)∣x∣α−1x = 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. [ABSTRACT FROM AUTHOR]