Transversality conditions for the existence of solutions of first-order discontinuous functional differential equations
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Published:2021-09-12
Issue:
Volume:
Page:1-17
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ISSN:1230-3429
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Container-title:Topological Methods in Nonlinear Analysis
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language:
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Short-container-title:TMNA
Author:
Pouso Rodrigo LópezORCID,
Albés Ignacio MárquezORCID,
Rodríguez-López JorgeORCID
Abstract
We are concerned with the existence of extremal solutions to a large class of first-order functional differential problems under weak regularity assumptions. Our technique involves multivalued analysis and the method of lower and upper solutions in order to obtain a new existence result to a scalar Cauchy problem. As a consequence of this result and a monotone iterative method for discontinuous operators, we derive our main existence result which is illustrated by several examples concerning well-known models: a generalized logistic equation or second-order problems in the presence of dry friction.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Subject
Applied Mathematics,Analysis