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2021 Transversality conditions for the existence of solutions of first-order discontinuous functional differential equations
Rodrigo López Pouso, Ignacio Márquez Albés, Jorge Rodríguez-López
Topol. Methods Nonlinear Anal. 58(1): 1-17 (2021). DOI: 10.12775/TMNA.2021.001

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.

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Rodrigo López Pouso. Ignacio Márquez Albés. Jorge Rodríguez-López. "Transversality conditions for the existence of solutions of first-order discontinuous functional differential equations." Topol. Methods Nonlinear Anal. 58 (1) 1 - 17, 2021. https://doi.org/10.12775/TMNA.2021.001

Information

Published: 2021
First available in Project Euclid: 21 September 2021

Digital Object Identifier: 10.12775/TMNA.2021.001

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.58 • No. 1 • 2021
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