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


Authors: Pierpaolo Omari and Fabio Zanolin
Journal: Proc. Amer. Math. Soc. 117 (1993), 125-135
MSC: Primary 34B15; Secondary 47H15
DOI: https://doi.org/10.1090/S0002-9939-1993-1143021-2
MathSciNet review: 1143021
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the periodic problem

\begin{displaymath}\begin{array}{*{20}{c}} { - u'' = f(u) + h(t),} \\ {u(0) = u(2\pi ),\qquad u'(0) = u'(2\pi ),} \\ \end{array} \end{displaymath}

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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DOI: https://doi.org/10.1090/S0002-9939-1993-1143021-2
Article copyright: © Copyright 1993 American Mathematical Society

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