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In this paper we will prove the coexistence of unbounded solutions and periodic solutions for the asymmetric oscillator x + f(x) + ax + - bx - = φ(t, x), where a and b are positive constants satisfying the nonresonant condition 1/√a + 1/√b ∉ Q and φ(t, x) is 2π-periodic in the first variable and bounded.

Unbounded solutions and periodic solutions for second order differential equations with asymmetric nonlinearity