Abstract
We obtain existence an multiplicity of harmonic and subharmonic solutions to the periodically forced nonlinear Duffing′s equation x″ + g( x) = p( t) in the semi-linear case: 0 < A ≤ g( x)/ x ≤ B < + ∞, for | x| large. We introduce new conditions of nonresonance with respect to the spectrum of the associated linear differential operator x↦ − x″ and show, by some nonlinear counterexamples, that the results are sharp.
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