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We study the periodic solutions of Duffing equations with singularities x" + g(x) = p(t). By using Poincaré-Birkhoff twist theorem, we prove that the given equation possesses infinitely many positive periodic solutions provided that g satisfies the singular condition and the time map related to autonomous system x" + g(x) = 0 tends to zero. [ABSTRACT FROM AUTHOR]

This paper establishes the existence of periodic solution for a kind of second-order singular nonautonomous coupled systems. Our approach is based on fixed point theorem in cones. Examples are given to illustrate the main result. [ABSTRACT FROM AUTHOR]

We study the existence of periodic solutions of the second-order differential equation x" ax+ + bx- + g(x(t - τ)) = p(t), where a, b are two constants satisfying 1/va+1/vb = 2/n, n ∊ N, τ is a constant satisfying 0 = τ < 2π, g, p : R R are continuous, and p is 2π-periodic. When the limits limx±8 g(x) = g(±8) exist and are finite, we give some sufficient conditions for the existence of 2π-periodic solutions of the given equation. [ABSTRACT FROM AUTHOR]