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Zeitschrift für Analysis und ihre Anwendungen


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Volume 39, Issue 2, 2020, pp. 131–150
DOI: 10.4171/ZAA/1654

Published online: 2020-04-07

New Fixed Point Theorem for Discontinuous Operators in Cones and Applications

Jorge Rodríguez-López[1]

(1) Universidade de Santiago de Compostela, Spain

We provide new fixed point theorems for a class of discontinuous operators by combining a new fixed point theorem of compression-expansion type for these discontinuous operators with monotone iterative methods. As an application we study the existence of positive solutions for a nonlinear fourth-order discontinuous boundary value problem.

Keywords: Fixed point index theory, Krasnosel'skiitheorem, discontinuous differential equations, fourth order problem

Rodríguez-López Jorge: New Fixed Point Theorem for Discontinuous Operators in Cones and Applications. Z. Anal. Anwend. 39 (2020), 131-150. doi: 10.4171/ZAA/1654