Boundedness in Nonlinear Oscillations at Resonance

Abstract In this paper, we are concerned with the boundedness of all the solutions for the semilinear Duffing equation x ″+ n 2 x + φ ( x )= p ( t )with the Lazer–Leach condition, where p ( t ) is a smooth 2 π -periodic function and the perturbation φ ( x ) is bounded.

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