Abstract :
In this article we propose how to define the Fu ik spectra for differential systems in nwith jumping nonlinearities. The PropertyP, a generalization of the non-Fu ik spectra to positively homogeneous nonautonomous differential systems, is also defined in the most general setting. A quantitative estimate result concerning the parameterized completely continuous, positively homogeneous perturbations of the identity in Banach spaces is given in this article. Such a result is a generalization of one property in the spectrum theory for completely continuous linear operators. Using this estimate result, we will give some significantly improved nonresonance results from the Fu ik spectra and PropertyPfor asymptotically positively homogeneous differential systems.
