Abstract

We consider the periodic problem\[−u=f(u)+h(t),u(0)=u(2π),u′(0)=u′(2π),\begin {array}{*{20}{c}} { - u = f(u) + h(t),} \\ {u(0) = u(2\pi ),\qquad u’(0) = u’(2\pi ),} \\ \end {array}\]and prove its solvability for any givenhh, under new assumptions on the asymptotic behaviour of the potential of the nonlinearityff, with respect to two consecutive eigenvalues of the associated linear problem.

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