Parametric monotone generalized equations in reflexive Banach spaces.
Periodic solutions of systems with asymptotically even nonlinearities.
Perturbed Hammerstein integral inclusions with solutions that change sign
We establish new existence results for nontrivial solutions of some integral inclusions of Hammerstein type, that are perturbed with an affine functional. In order to use a theory of fixed point index for multivalued mappings, we work in a cone of continuous functions that are positive on a suitable subinterval of . We also discuss the optimality of some constants that occur in our theory. We improve, complement and extend previous results in the literature.