Coupled fixed points of multivalued operators and first-order ODEs with state-dependent deviating arguments |
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Authors: | Rubé n Figueroa ,Rodrigo Ló pez Pouso |
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Affiliation: | aDepartamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Sur, 15782 Santiago de Compostela, Spain |
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Abstract: | We establish a coupled fixed point theorem for a meaningful class of mixed monotone multivalued operators, and then we use it to derive some results on the existence of quasisolutions and unique solutions to first-order functional differential equations with state-dependent deviating arguments. Our results are very general and can be applied to functional equations featuring discontinuities with respect to all of their arguments, but we emphasize that they are new even for differential equations with continuously state-dependent delays. |
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Keywords: | MSC: primary 34K05 |
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