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arXiv · 1509.08653

Double resonance for one-sided superlinear or singular nonlinearities

Andrea Sfecci
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Abstract

We deal with the problem of existence of periodic solutions for the scalar differential equation x" + f (t, x) = 0 when the asymmetric nonlinearity satisfies a one-sided superlinear growth at infinity. The nonlinearity is asked to be next to resonance and a Landesman-Lazer type of condition will be introduced in order to obtain a positive answer. Moreover we provide also the corresponding result for equations with a singularity and asymptotically linear growth at infinity, showing a further application to radially symmetric systems.

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Andrea Sfecci. 2015-09-29. Double resonance for one-sided superlinear or singular nonlinearities. https://doi.org/10.1007/s10231-016-0551-1

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