Open AccessTransversality conditions for the existence of solutions of first-order discontinuous functional differential equations
Author(s) -
Rodrigo López Pouso,
Ignacio Márquez Albés,
José Daniel Gómez López
Publication year - 2021
Publication title -
topological methods in nonlinear analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.623
H-Index - 23
ISSN - 1230-3429
DOI - 10.12775/tmna.2021.001
Subject(s) - mathematics , monotone polygon , transversality , scalar (mathematics) , order (exchange) , class (philosophy) , initial value problem , mathematical analysis , differential equation , ordinary differential equation , geometry , finance , artificial intelligence , computer science , economics
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.