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In this paper we deal with semilinear problems at resonance. We present asufficient condition for the existence of a weak solution in terms of theasymptotic properties of nonlinearity. Our condition generalizes the classicalLandesman-Lazer condition but it also covers the cases of vanishing andoscillating nonlinearities.

Landesman-Lazer condition revisited: the influence of vanishing and oscillating nonlinearities