Abstract: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 $[0,1]$. We also discuss the optimality of some constants that occur in our theory. We improve, complement and extend previous results in the literature.
Keywords: fixed point index, cone, nontrivial solution
AMS Subject Classification: 45G10 34A60 34B10 47H04 47H10 47H30