A conjecture on fixed-point indices of mappings in cones

In this paper, we will study a conjecture on fixed-point indices of mappings in cones proposed by Dancer. Adding the assumptions that the cone has nonempty interior and one of the generalized eigenspaces of the operator, whose corresponding eigenvalue is greater than 1, intersects the interior of the cone, we shall prove the conjecture. [Copyright &y& Elsevier]