Double resonance for one-sided superlinear or singular nonlinearities

TL;DR

This paper investigates the existence of periodic solutions in scalar differential equations with one-sided superlinear or singular nonlinearities, introducing new resonance conditions and extending results to singular and asymptotically linear cases.

Contribution

It introduces a Landesman-Lazer type condition for one-sided superlinear and singular nonlinearities, extending the theory of periodic solutions in nonlinear differential equations.

Findings

Existence of periodic solutions under new resonance conditions

Extension to equations with singularities and asymptotically linear growth

Application to radially symmetric systems

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.