Solutions of nonlinear equations in cones and positive linear operators
- Autores: J.R.L. Webb
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 82, Nº 2, 2010, págs. 420-436
- Idioma: inglés
- DOI: 10.1112/jlms/jdq037
- Enlaces
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Resumen
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.
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