Resumen de Solutions of nonlinear equations in cones and positive linear operators

J.R.L. Webb

• We introduce a modification of the concept of a cone invariant linear operator being u0-positive, a concept due to Krasnosel�fski... We show how this definition allows us to prove results closely related to some results for positive operators in a classic text of Krasnosel�fski... We also show how it can be used, in conjunction with the theory of a fixed-point index, to give some short proofs of existence and nonexistence of positive solutions for nonlinear maps. We prove a new fixed-point index result and show that it can be applied in cases where the previous theory is not applicable.