Nonresonance conditions on the potential for a second-order periodic boundary value problem

Omari, Pierpaolo; Zanolin, Fabio

doi:10.1090/S0002-9939-1993-1143021-2

Nonresonance conditions on the potential for a second-order periodic boundary value problem
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by Pierpaolo Omari and Fabio Zanolin

Proc. Amer. Math. Soc. 117 (1993), 125-135

DOI: https://doi.org/10.1090/S0002-9939-1993-1143021-2

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Abstract:

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

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