Transversality conditions for the existence of solutions of first-order discontinuous functional differential equations
DOI:
https://doi.org/10.12775/TMNA.2021.001Keywords
Discontinuous differential equation, functional differential equation, monotone iterative methodAbstract
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.References
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