We deal with the problem of existence of periodic solutions for the scalar differ- ential 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.
Double resonance for one-sided superlinear or singular nonlinearities / Sfecci, Andrea. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 195:6(2016), pp. 2007-2025. [10.1007/s10231-016-0551-1]
Double resonance for one-sided superlinear or singular nonlinearities
SFECCI, Andrea
2016-01-01
Abstract
We deal with the problem of existence of periodic solutions for the scalar differ- ential 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.